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 Fan Dumb 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.
Furthermore, it's been revealed that Aizen had manipulated Ichigo's development, including the very first meeting between himself and Rukia. Naturally, this upset many Ichiruki shippers, who wildly denied such a declaration, but Aizen himself was finished off by Ichigo at the end of the Deicide arc, so they won't disparage him as much either. In both cases, instead of the typical Ship-to-Ship Combat, shippers were just peeved that another character 'disproved' the "certainty" of Ichigo getting together with Rukia.
This is, of course, assuming Aizen's claim of having been manipulating Ichigo's entire life is actually true and not a lie he made up to mess with Ichigo's head.
It is also rather silly. Just because a character arranged for a meeting does not mean that all the emotions and development between those characters is automatically rendered invalid.
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), 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.
Reaches its more idiotic, misogynistic and almost horrifying extreme when rabid IchiRukis make truly mindboggling assumptions about Orihime Fighting From The Inside against Tsukishima's brainwashing. Such a fact somehow makes her a "shallow whore" and a "selfish bitch", whose care for Ichigo is "utterly pathetic" and "will never compare to Rukia's Eternal and Mature Love.
And if you look at the discussion page for this section, well... the rabid Ichigo/Rukia fans are so threatened by Orihime that they've also trolled this very wiki to attack the character, the Ichigo/Orihime pairing, and the fans of both.
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. Granted, it happens less than Orihime bashing, but still...
Actually, Renji hate has always been here and there. 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 (nevermind that Byakuya was in charge and thus Renji was bound to be there whether he wanted or not), 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 havbe trouble for having bonds to someone under her new social status), etc. Threfore, for these people Renji is a massive, idiotic loser who will never measure up to Rukia's Perfect Man Ichigo and is considered as a possible love interest for her only by those who want to split up Ichigo and Rukia.
For many reasons, some Renji/Ichigo fans can get batshit crazy and bash both Orihime and Rukia. Don't ask.
Poor Uryuu 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.
And recently many rabid Ulquiorra/Orihime fans have joined in the Ship-to-Ship Combat against Ichigo/Orihime (and sometimes even Renji/Rukia). 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 Ulquorra/Orihime fans who actually ship the pair and don't give a damn about Ichigo/Rukia.)
Read this UlquiHime essay. Pick up the Unfortunate Implications it brings. Ulquorra's feelings for Orihime? Complete and Absolute ~True Love~ that should never be denied or challenged because Ulquiorra is pretty much God. Orihime's feelings for Ichigo, including her Anguished Declaration of Love? Total little girl shit that doesn't matter unless it's to point how immature and horrible she is. Eeeeeeew.
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.
Some of the most rabid Momo Hinamori 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.
A very, very welcome subversion comes along the lines of Ichigo/Nelliel. Neither the IchiHime nor the IchiRuki 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 Girland 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.
Subverted with Riruka Dokugamine; none of the Ichigirl pairings have attacked her for being interested in Ichigo, mainly due to how Hilarity Ensues whenever she expresses it around him.
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.
Tatsuki is mercifully spared from this, except by fans who do not have all their marbles. Tatsuki has done nothing to earn the ire of either Ichi Hime or Ichi/Ruki fans, and it also helps she is considered a secondary character by the fandom at large. However, if that does change...
Actually, she's often used as the incarnation of this trope. While she doesn't get directly bashed in fanwork, she's sometimes chosen as the mouthpiece of choice for IchiHime bashers, who then make her tell Orihime that she should fall out of love with Ichigo and go for others instead — basically putting their own Ichigo/Orihime bashing in Tatsuki's mouth, nevermind that nothing in canon says Tatsuki would disagree to having two of her closest friends hook up...