Can they get along with both Ichigo and each other?
Whenever a Shōnen has an Estrogen Brigade amidst their fandom, it's inevitable for a shipping war to ignite the mere second that a character interacts with another. What makes Bleach especially notable, however, is how the het fans are the ones causing the most amount of controversy around these parts.
Here comes a weird variant. The Ichi/Ruki shippers used something along the lines of "their meeting was destiny" as their tagline, even claiming that Ichigo was Kaien's reincarnation. The latter point was proven false ever since Aaroniero revealed that Kaien was trapped inside Aaroniero himself, after the latter absorbed Metastacia, a Hollow that fused with Kaien. Reactions varied within the fandom, but the shippers were most affected by that revelation; Ichiruki shippers were outraged, while Ichihime shippers saw it as a Take That. Since Aaroniero actually was killed by Rukia shortly after that reveal, the shippers aren't as likely to shout at Aaroniero these days.
Ever since OrihimeInoue started to take a bigger role in the storylineand was revealed to actually be in love with Ichigo as well as MUCHmore powerful than anybody would think, militant and enraged Ichigo/Rukia fangirls twist her into a Rukia-hating, Ichigo-obsessed stalker to make Rukia look like a better match for him. Never mind that Orihime is the depressedand passive kind of jealous, that she adores Rukia (to the point of actively rejecting the idea of hating her, as well as praising Rukia's kindness and strength), that she actually got over it as she got more spotlight and development, and that Rukia herself adores Orihime and sees her own issues reflected in her. This has become so bad that everyone in the Ichigo/Rukia corner has been stereotyped as Orihime bashers, including sane ones who like or at least don't mind Orihime and only hate the idea of being lumped with the crazies.
Some militant Ichigo/Orihime fans also do this, painting poor Rukia in a horrible light by twisting her into an evil, possessive and bitchyYandere who wants Orihime dead and away from her boytoy and completely hates her old friend Renji Abarai for having some feelings for her, despite all evidence pointing towards how she deeply loves both of them. This runs contrary to the fact that bashing Rukia (and the Ichigo/Rukia pairing by extension) is forbidden in some Ichigo/Orihime circles because the majority actually likes Rukia.
Speaking of Renji, some twist both him andByakuya into wife-beaters, rapists, etc. to favor the Ichigo/Rukia coupling. It's much more passive-aggressive than the loud and misogyny-based Orihime hate, though: the culprits tend to say Renji doesn't deserve Rukia's prospect romantic feelings for having contributed to her arrest (never mind that Byakuya was in charge and thus Renji was bound to be there whether he wanted or not, which caused him quite a bit of angst), whine because he stepped out of her life for years after she was adopted by the Kuchiki clan (because it's not like he thought that Rukia would have trouble for keeping bonds to someone who was under her new social status), etc. Therefore, for these people Renji is a massive, idiotic, woman-hating loser who will never measure up to Rukia's Perfect Man Ichigo and must have been considered as a possible love interest for her only by those who want to split up Ichigo and Rukia (Never mind all the Ship Tease between Rukia and Renji themselves, how Renji is revealed to be very devoted to Rukia once their common backstory is revealed, or even the scene where Renji takes a HUGE risk via challenging Ichigo to "punish" him for putting Rukia at risk, and once he loses, he begs Ichigo to save her in his stead).
For many reasons, some Renji/Ichigo fans can get batshit crazy and bash both Orihime and Rukia. Don't ask. Take Our Word for It.
Poor Uryu Ishida gets it from rabid fans from all sides. The Ichigo/Rukia section blames him for failing to seduce Orihime and make her forget about Ichigo (no matter how out of character that would be), and more recently, for assisting her in an endeavour where she ended up saving Ichigo's life (instead of their Possession Sue version of Rukia) and Ichigo went berserk to protect her. Those in the other camp insist he is a) not good enough for their darling, pure and perfect goddess and/or b) a douchebag that doesn't let Orihime fight for herself, never mind that everybody (save for Rukia and Chad) wants her to keep out of fights.
Many rabid Ulquiorra/Orihime fans have joined in the Ship-to-Ship Combat against Ichigo/Orihime (and sometimes even Ulquiorra/Grimmjow). Surprisingly they never seem to actually defend Ulquiorra/Orihime; in fact, their level of sheer and utter hatred for Orihime and the Ichigo/Orihime pairing sometimes reaches scary levels, and one has to wonder just why they claim to ship a pairing that involves someone they hate so much. (The answer is, of course, that most of them rabidly ship Ichigo/Rukia and treat Ulquiorra/Orihime as only Ship Mates, much to the annoyance of real Ulquiorra/Orihime fans who actually ship the pair and don't give a damn about Ichigo/Rukia.) Meanwhile, the more level-headed Ulquihime fans who disagree with the ones above wish that the Vocal Minority would stop giving the bulk of the fans a bad name.
Heck, even Ulquiorra/Orihime gets its fair share of bashing. Such as people attacking the pairing and Orihime in general by drawing Orihime getting her head ripped off. And with almost 5,000 downloads of the drawing, too. This is most likely hatred coming from fans who want Ulquiorra with someone else or just hate Orihime with him because they believe she's holding him back.
Momo Hinamori: Some of her most rabid haters are Hitsugaya/ Matsumoto shippers who have somehow convinced themselves that Hitsugaya isn't allowed to care for two girls at the same time (even if it's in different ways) and must choose between his sexy and self-assured lieutenant and his brokenadoptive sister and then run the girl he doesn't pick with his own sword. Or maybe that's because those fans also happen to hate Hinamori, even if she's not paired with Hitsugaya at all. And finally, she's not safe from het-pairing lovers only: Momo is also often bashed for the sake of some yaoi pairs, like Aizen/Gin. It doesn't end there. Momo is likewise the main target from Hitsugaya/Matsumoto shippers for - you guessed it - being SO loyal to Aizen, that she was in traumatized denial of his betrayal for quite some time after he stabbed her. Because how dare she be affected by all the shit she went through and react like a normal person would.
A very welcome subversion comes along the lines of Ichigo/Nelliel. Neither the Ichi/Hime nor the Ichi/Ruki shippers have ever attacked Nelliel for her affectionate behavior towards Ichigo. In fact, most of them actually like Nelliel, and a few even have her as a sub-pairing that they enjoy toying with in some fanart or fanfiction. It helps that she's both a Genki Girl and an Action Girl.
As a warning, don't ever bring up Senna in a conversation. Despite only appearing in one film, her chemistry with Ichigo provoked a lot of attacks from shippers of both Ichigo/Rukia and Ichigo/Orihime, but since she's never featured in any other Bleach-related media, outside of the first movie, a video game and a cameo in episode 204, the hate for her (thankfully) isn't as frequent or heated. Then again, one only needs to click on a fanart of the pairing or see the Memories of Nobody movie on Youtube to find someones' loathing for it and Senna.
Tatsuki does not have any real hate for her character, considering she is considered a secondary character by most of the fandom and no threat to either of the major ships. The problem comes when the fanatics of the major pairings use her as a tool in their shipping wars because of her friendship with Orihime. One rabid Ichi/Ruki side uses her as a mouthpiece to express their dislike of Ichi/Hime, while other Ichi/Hime fans claim that Tatsuki supports Ichi/Hime and make claims that Tatsuki would be upset with or automatically hate Ichigo if he rejects Inoue, essentially using her character the same way as detractors would: an anti-pairing tool.
And the recent Everything but the Rain flashback arc has brought another victim: Kanae Katagiri, Ryuuken Ishida's sort-of fighting partner, and who would eventually become Uryuu Ishida's mother. At one point she decided to tell Ryuuken's mother that his then-arranged girlfriend, Masaki Kurosaki, had fought a Hollow without her input and was injured because of it, despite Ryuuken himself asking her to keep the secret; imediately, a small but very local part of the fandom started screaming for Kanae's blood, accusing her of ratting Masaki out due to petty jealousy over her being Ryuuken's wife-to-be. Nevermind that she did it to get Masaki help since she had been developing a Hollow hole due to said injury and genuinely thought she was fulfilling her duty.
It doesn't help that the entire Bleach series is a) long running, b) Shonen, and c) likes to draw out its action scenes. Oh, and the mangaka likes to keep things intentionally vague about relationships for some reason (even Naruto has more relationship development). Hence people with preferred characters start to pick and choose to enhance relationship development. Word of God has said that he feels that the characters have more potential than just falling in love. Then again, this comes from the author that has also openly said the more hate Orihime gets, the more screen-time he gives her.