Depends on the language. A language that is not controlled by a steering institution (see https://en.wikipedia.org/wiki/Acad%C3%A9mie_Fran%C3%A7aise) will float freely, evolving as it does by public use of words. If I use a word and you understand it, then it is a word. Definitions also float in this way.

But the argument for/against politically correct language can be interesting. Because, unlike a controlling organization, there is instead social pressure being applied. And you may disagree with the source of that pressure, politically. Sometimes it makes you an asshat, and sometimes it's legitimate pushback.

Anyway, long short, I don't think there's anything fundamentally wrong with it. Nor do I think it's weird that some people push back.