To a certain extent it makes sense. Groups like the Avengers need to look out for the entire planet, not just mutankind. Sometimes what's best for mutants isn't what's best for the rest of the world. Avengers vs. X-men is almost a good example of this, except the writing is atrocious and everyone acts like children.
I'd like to see some nuance, or at least more details, on why there's been such a split between other heroes and mutants. Something more than Cyclops thumbing his nose at other heroes for not helping more. How about, after AvX, heroes saw Scott escape from jail, and were just wary of him and the mutant groups he lead. At that point several mutant groups started doing increasingly sketchy things and working more and more with mutant villains. They were in a 'whatever it takes' kind of mindset, which made it harder to see them as pure heroes, and their conflicts got more grey.
Then Inhumans vs X-Men happened, which was also badly written, but involved the X-men going on the offense without bothering to talk or explain the problem to other groups. We saw in other stories that most heroes saw it as 'escaped convict Scott Summers went off the deep end and tried to screw over the Inhumans', leading to those stupid 'mutant Hitler' lines. That debacle ended with Emma Frost obliterating two Inhuman cities and siccing the Sentinals on the Inhumans.
X-men Gold and Blue came next, and while in Gold they tried to integrate more with regular humans with the school in central park, there were problems. In Secret Empire, Emma led the mutants into siding with Hydra, and gave some token help to the resistance while actively attacking the Secret Warriors. In the end, she gave away a Cosmic Cube shard to the Nazis, and only joined the final fight when things were falling apart. The mutants we saw were mostly OK with what she had done, despite her being a war criminal and mass murderer. After that some mutants like Kate played lip service to her being a criminal, while Iceman was totally OK with paling around with her. In Blue, Emma also helped bomb multiple cities around the world to forcibly make more mutants, and again only stopped when it was clear she was going to lose. Again, she suffered no consequences, and she was in fact shielded by the X-men for vague "we will need her later" reasons.
Then came the Poison event, where the Blue team helped draw the Poisons to Earth. They were targeting Earth anyway, but the X-men exacerbated it by letting Jean get absorbed by them. Following that was Dissassembled and Age of X-man, which were massive disasters caused by mutant infighting and confusion. At no point did the X-men ask for help. Instead, most of them were presumed dead at the hands of X-man. Right after that, convicted murderer Cyclops turns up alive and well, leads a small team all over picking fights with some villains and working for others. Eventually, Emma Frost mind controls the entire world into forgetting and ignoring mutants entirely, and mind controls the Avengers specifically to distribute a cure for a mutant vaccine. The remaining X-men are mostly OK with this, until the people from Age of X-man come back. Immediately afterwards, Krakoa becomes a thing out of nowhere.
If I mischaracterized or misremembered or left something out of all that, please feel free to correct me. My point in all that is that you can extrapolate from all of that stuff that the rest of the superhero community could see all of that and decide to keep the X-men at arms length. Buddying up to Emma Frost alone would cause the Avengers to react with horror. This hasn't been stated in text, but I've been assuming its playing a part. I also vaguely remember several character telling other heroes "mutants handle mutant problems" but I can't remember that happening specifically and might be wrong.