Ayu from 7 Seeds can have shades of this. She calls people "resistant as cockroaches", but means it in the nicest way of a compliment. She decides on a group-split-up that leaves her with someone that she is implied to have a crush on and doesn't get it why people react strangely about it. It isn't until Tsunomata points out to her that her straightforward ways can be seen as hurtful that Ayu even wonders why it would seem hurtful.
Eijun Sawamura, the protagonist of Ace of the Diamond, has a habit of judging people based only on what he knows, but he's never cruel on purpose. An example of this was as when he was paired with Chris for training, and found Chris' apparent lack of motivation and gloomy attitude annoying, even accusing him of not trying hard enough to get to Seidou's first string. Then, Sawamura learns that Chris once was Seidou's star catcher, but suffered a shoulder injury that put him out for a whole year, and since then he's been undergoing rehab while clinging to the hope of being able to play once more. Sawamura feels horrible upon learning this, even more when he understood that Chris' words of "Don't end up like me" meant "Don't risk yourself to suffer an injury that ruins your future career".
This is what kicks off the plot of The Anthem of the Heart: as a child, Jun Naruse witnesses her father leave a gaudy building made to look like a fairytale castle accompanied by a woman she's never seen before, and immediately comes to the conclusion that he's secretly a prince- and promptly goes to tell her mother. As Jun gushes about her father and "his princess", her mother's back is to the camera, but her reaction is more than clear to the viewer.
Misa's "experiment" on Ao in Chapter 7 / Episode 3 smacks of this. What she wants is to know whether Ao gets close to everyone, or just to Mira. She does this in a way that Moe mistakes her for seducing Ao, and both Ao and Mira are not pleased by her explanation that Ao was her "guinea pig", especially when Ao nearly gets a panic attack from Misa.
Yuu "Nana" Nanami speaks her mind without reading the room. For example, in Chapter 34, when the results come back for the Shining Star Challenge applications- Mira passed and Ao failed- the first thing she wonders aloud is why it is Mira, rather than Ao who passes it. Chikage has to shut her up for rubbing salt into their wounds.
Laios of Delicious in Dungeon can be this sometimes. His love for everything monster-related leads him to do and say questionable things. In one chapter where everyone is stripping down out of their wet clothing, he wants to see a naked Itsuzumi. Not for any sexual reasons, but to see how her fusion with an animal soul has affected her body. He is still forced to wear a blindfold by the others for the rest of the chapter.
When Loki Asgard transfers into the main characters' class in Boku Girl, her first act upon seeing the androgynous Mizuki is to remark on how girls are allowed to wear the boys uniform. This is actually a subversion in that Loki Asgard is the Loki and is directly responsible for Mizuki being turned into a physical girl, so she knows exactly what she's saying.
While Seigi of The Case Files of Jeweler Richard is a kind person and usually bears no ill will towards others, he has the tendency to speak without taking into consideration how his speech might affect the other person, making him come off as rather pushy at times (and an Innocent Bigot at worst). Richard even calls him out for this, and he works to get better.
Ian in A Cruel God Reigns does this to Jeremy when he actively tries to make their new step-family a happy one. What he doesn't know is that his father is sexually abusing Jeremy every weekend when they come home from their boarding school.
Ian: The plan is to make this a loving household of Lynn Forest, aiming to create a peaceful family. Jeremy: Will it all... work... out? Ian: We'll make it work Jeremy! And in the end, we'll all be happy.
Although Anri of The Demon Girl Next Door means well for Yuko, she has a habit of letting slip things that Yuko would rather not have mentioned, to the point where Yuko wonders if Anri secretly has it in for her. This is why Yuko sometimes says she's an assassin.
An episode of Digimon Adventure was focused on Mimi getting into trouble after she got upset at Izzy, who ignored her in favour of working on his laptop. He had no idea why she was crying, or that he'd been ignoring her at all.
Patamon causes a fight with TK later by not realizing how serious it was that his partner wasn't going to be able to be with Matt for a while due to their parents being divorced.
Terriermon in Digimon Tamers combines this with Brutal Honesty, occasionally having to be reminded by Henry in early episodes that what he's saying is rude.
Devils from Dorohedoro have this as one of their hats. Then there's the Magic User Kawajiri, who has difficulty being tactful due to having spent years as a devil himself.
In Dragon Ball, Goku often tells Bulma how useless she is and even looks under her skirt trying to find, depending on the version, either her tail or her balls. During his adventure to find the Dragon Balls, he gets into the habit of patting a person's crotch when he meets them to find out their gender. He grows out of it, but he never stops being bluntly honest in his evaluation of other people's ability to fight or even just contribute.
Though it's implied that he had brain damage as a baby due to hitting his head, and not to mention he was almost totally isolated from others until he was 12.
Maron, a filler character, in the Garlic Junior Saga of Dragon Ball Z, is this when she insults Chi-Chi and Bulma by calling them old ladies (and you can guess how the former reacts).
Little Marron, Krillin & Android 18's daughter, also qualifies. In a scene in the Great Saiyaman Saga, when Master Roshi asks if he wants to participate in the tournament, she replies with "No way, you're too old!!". For Marron, this is a Justified Trope, as she is only 3 years old and she doesn't know any better.
Shou from Father and Son tends to say things that offend people. He once unintentionally offended his teacher as well as his mother whom he had never met until that day. It may be justified since he's a little kid and doesn't know how to speak tactfully.
When Ryuuichi prepares himself to be Santa Claus for Kotarou, one of his classmates innocently remarks that should be a job for fathers. Only to be quickly called out because Ryuuichi and Kotarou recently lost their parents.
The children often don't understand the concept of tact, justified since they are just toddlers. One example is when they cheerfully call to attention how large Ushimaru's chest is.
In Girls und Panzer, when Ami, temporary tankery instructor for Oarai, sees Miho among the assembled students, she points out that Miho's mother (Ami's tankery instructor) has done quite a bit for her, makes a polite inquiry about how Miho's sister is doing and says the Nishizumi school has a long history. Despite having no ill intentions toward Miho, Ami ends up upsetting Miho by bringing up her family (Miho, unable to adhere to her family's Second Place Is for Losers mentality, had until recently quit tankery), but Saori quickly moves to Change the Uncomfortable Subject.
Guilty Crown: Shu really should have known better than to underestimate Ayase just because she was in a wheelchair. When he is told he will receive his training from her, he remarks on his unease about being trained by a disabled person. Ayase smiles, then offers a handshake, which Shu accepts... leading him to be knocked off his feet and thrown to the ground, where she coldly tells him that her only disability is dealing with people like him.
Miyako in Hidamari Sketch does this a lot. It's hard to be sure when she's just oblivious and when she actually is winding up Hiro.
Inuyasha's title character has his moments. Justified, since he is a half-demon and was treated rudely by humans and demons, decided to live isolated from others and hence doesn't know when something can be seen as rude.
An interesting example is that Aquawas intentionally ragging on Eris for padding her bra after defending Albedo being a virgin—with the unintentional part being insulting Aldebo's cohort Shalltear, who's just as prone to do the same thing Aqua was ragging on Eris for.
Aqua herself was on the receiving end of this after Aniz and Subaru calm Tanya after she came to believe Aqua was Being X, both with Subaru pointing out how pathetic Aqua is and Tanya realizing that because of this, Aqua couldn't be Being X.
I Think Our Son Is Gay: The boys' father Akiyoshi genuinely wants to bond with his teenage sons, but doesn't know Hiroki is gay and unknowingly makes some insensitive remarks about homosexuals. Fortunately the mother Tomoko is able to defuse the situation and gently tells him to be a bit more open-minded.
Imoko cheerfully introduces her sister as a NEET, since she doesn't know what that is.
Mrs. Niito gently suggests that Neeko's friend Uriko, who's also unemployed, worry about herself before Neeko. Uriko then replies that she had to quit her job because one of her superiors was sexually harassing her and that she's working on finding work again. Mrs. Niito then apologizes for being insensitive.
A really twisted example happens in JoJo's Bizarre Adventure: Stardust Crusaders. The team checks into a hotel run by Enya Geil, master of the Justice Stand and actually an assassin planning to kill them all one by one. Polnareff walks in on her while she's trying to dispose of a body, and starts talking about how she seems very lonely running the place on her own, and doesn't she have a son or a family, and wouldn't it be nice to have grandkids running around, and even offers to fill the void for tonight by pretending to be her son. Thing is, Enya had a son - J. 'Centerfold' Geil - whom Polnareff killed.note Of course, he was also an assassin, as well as a serial killer who had once killed Polnareff's sister, so he was definitely not an angel in anyone's eyes but his mother's. Enya is seething and fighting hard to keep from dropping the charade and just stab him there and then. And Polnareff just keeps smiling.
This was Kaguya's primary flaw as a child. Being The Ace, she naturally excelled at everything and mistook everyone else lagging behind her as deliberate laziness. Since she was punished whenever she made a mistake at home, she would always tell them to take things seriously, which invariably drove them away due to them thinking that she was looking down on them.
After Kaguya and Shirogane become a couple, she starts sharing the details of their relationship with Hayasaka, not realizing that she's essentially bragging about how awesome it is having a boyfriend to someone who's still single (and may have some feelings for Shirogane herself). She honestly thinks Hayasaka wants to hear all of this, and doesn't understand why she's started running away whenever Kaguya starts talking.
Due to her complete obliviousness over Maki's crush on Tsubasa, Erika believes that Maki's depression was caused by her not being able to spend time with Kashiwagi and attempts to cheer her up accordingly. This does far more harm than good, especially when she refers to Tsubasa as Kashiwagi's "destined partner".
Karen: What on God's green Earth is that girl doing!? She doesn't know a thing about love!
Played for Drama in Kotoura-san, when this trope, combined with telepathy that Haruka couldn't turn off, causes her to inadvertently start blurting out her friends' and family's personal secrets, resulting in her schoolmates labelling her as a freak and compulsive liar and her parents' divorce. Although later on she invokes this trope to keep people from being close to her.
When Suzu mentions his boyfriend in Love Me For Who I Am, Mogumo asks him if he's "homo". When the others correct Mogumo by telling them that "homo" is considered derogatory, Mogumo gets teary-eyed and apologizes.
Major: Ryoko Kawase makes a seemingly innocent comment about Joe Gibson's dead ball being the other player's fault for not dodging it. Given that the other player was Goro's father and it caused his death, this struck a very sensitive nerve on him.
In Mobile Suit Gundam SEED Destiny, After Shinn destroys the Freedom, apparently killing Kira in the process, he proudly walks up to Athrun and declares: "I got payback, for you and me both." Athrun responds by punching Shinn in the face. What Shinn didn't realize was that Kira is Athrun's oldest and best friend; as far as he knew, he was just taking out the guy who wrecked Athrun's Gundam and injured him pretty badly in the process.
In Monthly Girls' Nozaki-kun, Seo's jerkass attitude is seen by Nozaki as a result of being mood-blind. Probably the best example of this is when Seo tells Nozaki that people ask her for help all the time, that she's considerate of others, and that she can read situations...all while ruining a group picture, smearing someone's calligraphy, and interrupting a love confession, in that order. However, the rest of the time it's hard to tell whether she really is this trope or genuinely a jerkass. It seems like Seo tends to approach situations in the fastest, most practical way possible (like bluntly telling Kashima that her singing is god-awful) without thinking about the feelings of others.
Denki Kaminari openly called the villain Stain cool ... in front of Iida whose older brother was severely injured by Stain. However, once Midoriya pointed out the insensitivity of his remark, Kaminari quickly apologized.
Momo Yaoyorozu tends to forget that she is far wealthier than the rest of her middle-class classmates. She'll casually talk about her enormous mansion, the expensive tea brands she has available, and other such things without considering that her classmates don't have access to any of these privileges and have absolutely no idea what she's talking about. Her classmates don't mind, since she's Spoiled Sweet and it's obvious that she just doesn't understand that limited money is a thing that people have to deal with.
Inko Midoriya had a moment of this after a doctor informed her that her son was Quirkless, as she began crying and apologising to Izuku, which unintentionally made him feel much worse about the situation as it solidified that even his own mother doubted he could become a Hero without any powers.
Sakura combines it with Kick the Dog early on, mocking Naruto and declaring he became such a Bratty Half-Pint because he has no parents to teach him how to behave or tell him what to do. She does this right in front of Sasuke, the Sole Survivor of the Uchiha Clan massacre, who does not take it well and calls her out on it, berating her and telling her she has no idea what she's talking about.
Sai, post-HeelFace Turn and Character Development. He is trying to become better friends with Naruto and Sakura, but genuinely thinks "ugly" is a good idea for a nickname, and that people always need to hear the truth. Ironically when he decides to give this weird "sensitivity" thing a go, he decides the way to do it is to tell people the exact opposite of what he thinks of them, so he tells Ino she's gorgeous (thus making Sakura jealous). Even more ironically, they eventually end up married.
Setsuna in Negima! Magister Negi Magi tends to act far too formally and subserviently towards those she feels have a higher social class than her. For example, she always refers to her love interest as ojou-sama/milady and acts more like a servant than a friend. Konoka, for her part, keeps telling her to quit it to no avail. Near the end of the manga, she actually makes Asuna cry by acting even more subservient towards her than she does towards Konoka after Setsuna learns Asuna is actually a princess. Normally, she's Setsuna's best friend, which makes it quite painful to be treated like that. It was a slight exaggeration of how she really felt, but she wanted to make sure Setsuna cut it out immediately rather than make a habit of it.
Neon Genesis Evangelion: Rei once throws an Armor-Piercing Slap for saying some insulting things about Gendo, who has raised her for as long as she knows. She doesn't know that Gendo abandoned Shinji shortly after his mother died, and had every right to be pissed off at Gendo.
One Piece: Monkey D. Luffy's ability to do this is legendary. While in the tower of the Shrinking Violet mermaid princess, he starts eating her food while she talks to him. His mouth is filled with food, so his cheeks bulge out. This is new to the innocent girl, so she pokes his cheeks, and he shouts at her for it. She begins to well up with tears, and he calls her a coward, a crybaby, and says in a completely happy, joking manner, "I don't like you one bit!". He obviously thought he was bantering, since the next thing he says is to suggest she sneaks out of the room to go on an adventure, in as happy and joking a manner as before.
Sayaka is this to Kyousuke, the object of her affections. Kyousuke's passion is the violin, so his arm getting paralyzed in an accident was a big blow to him. Rather naively, Sayaka thinks bringing him classical music CDs would relax him. She was wrongnote because it was all music he couldn't play, and it sends him into tears at first and into an almost screaming Heroic BSoD later.
Akari: What's wrong? Didn't I praise him [Ryōga] enough? Ranma: You were praising him?
In The Red Ranger Becomes an Adventurer in Another World, Tougo wears his heart on his sleeve and never has any reservations about speaking his mind. Because of this, he tends to say things without thinking about how it could sound, proudly announcing that he defeated the Seed of Magic monster with his team's Victory Kizuna Buster despite how confusing that is. His forwardness also clashes with the strict social hierarchies of the fantasy world, and Rosie wants to kill Tougo for his constant lack of decorum towards Teltina (even though she's fine with it).
Usagi Tsukino. Due to her naivety, she has a habit of unintentionally offending others. In one episode, when Miss Haruna is hospitalized for being put into comatose, Usagi fails to understand the seriousness of the situation and tells the others that this is a good thing for her.
Gurio Umino. For example, when Usagi and Umino went to visit Naru after Nephrite's death, Umino casually said, "I thought you didn't go to school because you were sick, but I see it was just heartbreak," resulting in Usagi hitting him. Once they've gone out, he didn't take (or didn't seem anyway) into consideration Naru's feelings. Later on, however, he hinted to have felt bad because of this trope. Thanks to Character Development, he became a bit less of this trope later on. In the same scene, he tried to comfort Naru... by mentioning Nephrite's disappearance.
In Sazanka, Tatsuki and Aoi's mutual friend, whom the author calls "Friend A", has a habit of calling Tatsuki, who has Asperger's, "an aspie" when Tatsuki spaces out during conversations. The "Innocently" part comes into play when it turns out that Tatsuki never told Friend A, who'd heard someone use the term online and followed suit, not realizing what it meant.
Saya of Servant × Service tends to speak her mind without even considering the potential consequences. Particularly evident in Episode 6, where she unwittingly sent the normally carefree Yutaka into a Corner of Woe by passively saying that he's beneath her, and a flashback reveals that she rejected a boy's confession by saying he should've looked at himself in a mirror and thought again (she meant she thought he could do better). Eventually Chihaya had to warn her against rejecting Mrs. Tanaka's offer of marriage to her grandson so as not to cause heart attacks.
Masao from Shiki is mostly just a Jerkass, but there's many scenes where he comes off this way too.
Suzu from Snow White with the Red Hair manages to combine this with Brutal Honesty and Deadpan Snarker. It is incredibly difficult to tell when he's actually snarking but his questioning if he's going to be arrested when he learns that "Lowen" is actually the crown prince means he's not as innocent or oblivious to how out of line he tends to be as he tries to appear.
Nia in Tengen Toppa Gurren Lagann, due to her sheltered upbringing. She is completely oblivious to any negative mood, which doesn't endear her to the others, especially after Kamina had just recently died. She also cheerfully turned down Simon's proposal. Fortunately Kiyoh and Kiyal make her realize her accidental mistake.
In Tomodachi Game, Shibe's Establishing Character Moment demonstrates that he doesn't consider how his words come off as at times, and it remains a major flaw of his throughout the game. In a series where the reader is meant to doubt the characters, Shibe can come off as a Bitch in Sheep's Clothing or Jerkass in hiding, before it's made clear that no, Shibe's really just this trope.
Haru from Tsuritama tries to cheer up Yuki about his grandmother's hospitalization by telling him that everyone dies at some point. This is because Haru is a possibly immortal alien who struggles with understanding things from the viewpoint of us Puny Earthlings.
The titular character in Violet Evergarden, due to having No Social Skills as she lived her entire life as a Child Soldier. When meeting the Evergarden family for the first time, she bluntly proclaimed to their faces that she doesn't know what a "family" is and has no use for one. This initially causes Violet problems on the job, as her bluntness puts off her other co-workers and she inadvertently took a client's word at face value, writing her response to a love letter as negative and materialistic instead of coy.
Iris's mother simply couldn't understand why Iris was upset that she invited a number of boys to Iris's birthday party as a means to get Iris to marry one of them and settle back home. She also didn't understand why Iris was particularly uncomfortable with a particular boy who Iris specifically asked her mother not to invite (but she did anyways). Iris later revealed to Violet she confessed to that boy who gently turned her down, which is why Iris left for the city.
When Mako from Wandering Son went outside as a girl for the first time alone, she ended up running into her schoolmate, and crush, Oka. She panicked, ran away, and almost quit school to become a hikikomori, however she decided to confront Oka later. Oka didn't even notice her and states he couldn't imagine her as a girl anyway.
In Wonder Egg Priority, when Rika and Neiru first encounter Momoe, they both mistake her for a boy. Rika compliments "his" appearance, Neiru remarks that she didn't think boys were allowed to buy Wonder Eggs, and Acca and Ura-Acca merely state that boys can buy Wonder Eggs, without actually pointing out that Momoe isn't a boy. Momoe leaves and ends up bursting into tears.
Yachiyo likes talking to Sato about how cool Kyoko is and how much she loves and admires her. Since Sato loves Yachiyo, this is really unnerving him, but she doesn't realise that she is hurting his feelings because she is Oblivious to Love.
Takanashi Souta suffers from Cuteness Proximity in the presence of anything small, such as children, small animals, or Popura. So he can't help gushing about the latter small size despite the fact that she is complexed by it and would just love to be taller.
Yuuri's initial reaction to shattering Victor's heart is completely apathetic, reaching out to casually touch him while making an utterly inappropriate remark. He then proceeds to act confused and defensive when Victor snaps at him. Word of God also comments that he can be "quite cold-hearted", and is "someone who doesn't really try to get into people's hearts".
Victor's lack of experience as a coach causes him to be this, which results in him making Yuri cry by telling him that he'll resign being his coach if he doesn't place on the podium, which he only said to scare Yuri out of his anxiety. And, in Episode 11, when Yurio subtly mocks Yuri's performance by saying that Otabek will score higher than him, Victor doesn't defend Yuri or even give him some reassurance and simply expresses awe at Otabek's performance, which hurts Yuri even further. In fact, he says nothing to comfort Yuri even after seeing how he's upset with the results of his short program, though it's likely he's unaware that Yuri's mood is getting worse.
Yuuutsu-kun to Succubus-san: Eru the angel wants to help the depressed Yuu get back on his feet. Unfortunately, all she can do is encourage Yuu to do his best, unwittingly hit his Trauma Button, or otherwise offer empty platitudes. In contrast, the very first chapter shows Sakuma the succubus reading up on depression and discovering that telling people who tend to put blame on themselves "do your best" is the exact opposite of what's best to do, and one should instead tell them "you did your best."