I’ve discussed this in some depth over at Graphic Policy. A lot of this stems back from the way that the mutant metaphor was originally developed – early on, there’s just not that much exploration of anti-mutant prejudice that mutants need protecting from, so the emphasis in on this weird strategy of improving human-mutant relations by fighting evil mutants. (since the original idea was that mutancy was just an easy way to introduce a bunch of heroes and villains without having to think up individual origin stories) 

His biggest pro-mutant moment in the early comics is the X-Men taking down the sentinels. However, even then, you see Professor X engaging in a narrow form of activism – his first instinct when Bolivar Trask whips up an anti-mutant witch hunt is to engage him in an academic debate, trying to use his credentials as an expert to influence public opinion. It doesn’t go very well, even before Trask sends in the genocidal robots.

And when I have time to write my essays on how Claremont approached the mutant metaphor, you’ll see that this is kind of his main mode of political activism. He’ll testify against Senator Kelly’s Mutant Registration Act, he’ll engage in TV debates with Reverend Stryker, he’ll organize Magneto’s legal defense at the International Court of Justice, etc. And he’ll have his school, where he’ll educate several generations of mutants (OGs, Giant-Sized, New Mutants). 

But, in no small part because these are still superhero comics where the main event is introducing problems that can be solved with punching, we never see Xavier engaging in movement-building: we don’t see mutant rights groups being formed at a local, state, or national level, we don’t see a Mutant Equality Bill being proposed to counter the Registration Act, we don’t see Xavier leading protests or direct actions, etc.