Usagi in the 90's anime, who can be seen as either a naive but kind girl with faults, but a strong will to protect her loved ones, or a whiny, klutzy Sue that gets everything handed to her and steals all the attention away from the other characters. While some people are fine with her additional focus in the anime seeing as she is the main/title character, others are angry that the other girls' arcs and powers from the manga were cut out and they became less powerful with ineffectual attacks and easily taken down by threats in the anime before Sailor Moon finishes things. There's also the matter of Usagi becoming more naive, childish, and less capable in the anime compared to her manga counterpart, while also being more insecure, jealous, and possessive in regards to her relationship with Mamoru (most prominently seen in the third and fourth seasons), whereas in the manga, Usagi and Mamoru talked through their issues and established trust on both sides. Some find her anime characterization endearing and funny, while others find it annoying and concerning.
Chibi-Usa for multiple reasons, usually more of an issue in the anime than the manga though. In her initial appearances in R, she's often bratty and demanding, though the original English dub played this up much harder and cast Tracey Hoyt for her Sailor Moon R episodes. Not shockingly, she's more of a base breaker in the Western fanbase. There's also the matter of how Toei Animation made her an Ascended Extra in SuperS and the extremely popular Outer Guardians were Demoted to Extras for the course of the series. This also nearly killed the show off in Japan. None of this is the character's fault per se, but she does get blamed for it regardless. She also gets accused of having romantic feelings for Mamoru, her father. There's also the fact that she almost never seems to want to admit making mistakes of her own and often loves blaming Usagi for everything that goes on.
Mamoru. For starters, there are a lot of people who find the nature of their relationship as sweet due to their shared past. There are also a lot of people that find said shared past the only reason the two characters are together. There's also the matter of the break-up arc inflicted on him in the Sailor Moon R anime. While many fans pointed out that his reasoning in the arc was to actually protect Usagi, some other fans thought he was being unnecessarily nasty. The cheap resolution to the arc didn't help — they pull a Screw Destiny and get back together anyway... and the "threat" he thought he was protecting Usagi from never really materializes. His alter-ego Tuxedo Mask is also either adored by fangirls or loathed for being rather useless (his powers are throwing roses and... that's about it). In the anime, he doesn't get any of the character growth OR power growth he got in the manga that let him keep up with the main cast, and in fact downgraded after R to being mostly a supporting cast member and occasional Distressed Dude when the stakes needed to be raised. Oh, and all of this is before we even get to the blockback from the shippers who wanted Usagi to hook up with either Seiya in the final story arc or with Rei, or the crazy people who accuse him of being in love with his daughter. Then, there are some who disliked him from the beginning due to belittling and making fun of Usagi in a not so nice way.
Rei/Sailor Mars's 90's anime incarnation, notably the way she treats Usagi. While Usagi and Rei are frequently at odds in the anime, it's made clear by the end of the first series that they are in fact the closest people on the team and Usagi trusts Rei more than anyone else. However, many fans hate how the 90's anime changed her from an aloof, but kind friend to a hot-blooded, borderline abusive, hyper-critical bully who finds any opportunity to be a jerk to Usagi and in the first season, even tries to usurp leadership from Usagi to the point where she even bullies Ami into siding with her. While she has gotten somewhat better after the first season, she still take chances to belittle Usagi in every season to the point where there are people who wonder why Usagi is still friends with her. This carries over to debate about whether her personality was improved in Sailor Moon Crystal, with many fans saying that Rei's personality in Crystal is how she should be, and just as many saying that Crystal's Rei is far too meek and aloof. Though there is some hypocrisy in this, seeing as how these same fans adore Michiru's personality which is similar to manga/Crystal Rei's.
Haruka and Michiru: Some find them to be a pair of badass lesbians in a healthy relationship and love them for the skills and the class they carry, while others loathe that they became Adaptational Jerkasses and were needlessly antagonistic towards Sailor Moon and the Inner Guardians, producing unnecessary drama. For all their angst over how cruel it is that they have to sacrifice the lives of the talisman holders, they refused to consider any alternative options, going right to extremes from the word go, even refusing to cooperate with Sailor Moon and her team and share information with them which would have made things easier. They place all the blame on Usagi for the outcome of the battle with Pharaoh 90, but their aloof behavior, hasty decision making, and inability to cooperate and share meaningful communication greatly contributed to the situation. Even more frustrating, earlier in the season, Neptune proposed working with them, but Uranus shot her down. There's also their decision to defect to Galaxia's side in an attempt to trick and kill her led to a great deal of fans turning on them. Especially because they actually killed Saturn and Pluto in the process, which many feel is just unforgivable. The fact that they accomplished nothing made things even worse.
That said, it doesn't take away from their popularity. The NHK poll that was broadcast in December 5th, 2020 (which listed the top 50 characters, and each alter ego is counted as a separate character), they managed to get into the top 15, with Sailor Neptune being ranked 14th, Michiru being 6th, Haruka being 3rd and Sailor Uranus being 1st. Compare that to Usagi and her three alter egos, with Neo-Queen Serenity being 34th, Usagi being 15th, Princess Serenity being 13th and Sailor Moon being 2nd, Haruka/Uranus and Michiru/Neptune still manage to top most of them, if not all.
The Starlights in the anime where they have much more screentime and Seiya has become pseudo-love interest for Usagi. This tends to cause fights between people who like what the new set of characters bring or in particular people who like Seiya as the first serious alternative to Mamoru in the series, and people who don't like the new characters or the greater screentime they got in comparison to long-running cast members. And this is side-stepping the Die for Our Ship Seiya himself brings to the Usagi and Mamoru shipping quarters.
Mimete of the 90s anime has her fair share of fans who thought she was hilarious (especially because of the infamous Twister scene from episode 117), but she also has many detractors who loathed her for killing fan favorite Eudial to steal her job and then not really doing anything important with her job afterwards. Note that this is also a case of Americans Hate Tingle, as Mimete is very popular in Japan, more so than Eudial.
Shingo. Some don't like him because they see him as nothing more than an obnoxious Annoying Younger Sibling, even though he didn't take it nearly as far as Chibiusa did. But he's also got his own fans because he genuinely cares, is kind of like a stand-in for male Moonies, and is one of the most rounded and developed civilians in the series. There's also the matter of his voice in Viz Media's new English dub. He's played by Nicolas Roye (Mikey Kudo from Digimon Fusion), a full grown man, instead of a girl like in the DiC dub. Some genuinely don't mind this casting choice and find that his acting improves in Shingo's focus episodes, but others are quite critical of said casting choice and find Julie Lemieux's performance to be superior.
Naru. For many fans, she's The Woobie because of all the times she gets attacked, her love Nephrite died and Usagi kind of abandons their friendship. Others see her as a Damsel Scrappy because they got tired of all the times she had to be rescued, and many who watched the original dub found her annoying because of her awful Brooklyn accent.
that was broadcast in December 5th, 2020 (which listed the top 50 characters, and each alter ego is counted as a separate character), they managed to get into the top 15, with Sailor Neptune being ranked 14th, Michiru being 6th, Haruka being 3rd and Sailor Uranus being 1st. Compare that to Usagi and her three alter egos, with Neo-Queen Serenity being 34th, Usagi being 15th, Princess Serenity being 13th and Sailor Moon being 2nd, Haruka/Uranus and Michiru/Neptune still manage to top most of them, if not all.