While I don't care to validate accusations of projection word choice absolutely matters to people.

Call someone an extremist or a radical and you'll automatically be clued into a villainous label regardless of what that person is even a radical or extremist about.

Call someone a supremacist or a racist and they will nine times out of ten bite back about it if they're Americans, even if the same people may not really care about being labeled sexists or carnists.

Call someone militant or oversensitive to imply the target is unreasonable and misaligned with "most people" who they can fall back on to assure themselves whatever they do is fine just for usually getting a pass.