It's an interesting, if circular debate, because the term 'political correctness' means different things to different people.
I don't see swearing as politically correct, although I don't think it adds anything and I wish they wouldn't bother.
I don't see gender equality as politically correct (Star Trek has always espoused gender equality in principle - are people annoyed they are actually started to show it on screen? That seems odd).
I don't see racial equality as politically correct (Star Trek has always espoused racial equality - we all love Uhura - are people annoyed because Star Trek should show a glass ceiling for black women? That seems odd as we had several Hispanic commodores in TOS and a black captain in STIV).
I don't see sexual equality as politically correct (Star Trek showed numerous incidents of people having sex with members of other alien species. If you weren't repulsed by that concept then relations between the same genders of the same species really shouldn't bother you).
Star Trek?s politics may or may not be politically correct but it hasn't been wholly consistent. The liberal Federation has a secret organisation breaking it's own rules for political gain. That's a bit distasteful as it implies that the liberal elite can only achieve nirvana on the back of deception, colonisation by the back door, and sometimes even murder. It's distasteful but it also gives our liberal heroes some to rise above, something to be better than, something to pit their wits against. It's good storytelling.
If you're a fan of right wing oligarchies, dictatorships, or corrupt democracies, look to the alien of the week, not Starfleet. This is where Picard are departing overtly from classic Trek. The Federation has to work to maintain its ideals. Our heroes must actively help in that endeavour. The goalposts have shifted slightly but a goal is still a goal.
The main protagonists are not thieves or murdering mercenaries (well, ok Seven is a bit but I digress).
I think it's fine to say that the direction in which they've decided to take Star Trek is not to your taste (I enjoy the Abrams' movies for their pace and spectacle but I feel that they largely missed the point). I think boldly declaring that it isn't Star Trek is just hyperbolic.
I do love that Star Trek is so diverse and invokes such passion in people that we take the time to have these conversations. In the 23rd century, we've learned not to fear words. ;-)