Is the destruction and annihilation of culture in the US inevitable?

[Rules for me, but not for thee]

If the left has their way, yes.  The right is fighting against multiculturalism (or maybe more monoculturalism, which is the endgame of the left's ideas). Of course the counter-argument is that these people are bigoted, racist, sexist, etc.

Is fighting for the existence of your culture really racist, sexist, or whatever? No. There are bigots in the group, yes but it's not the great majority of them.  People like to live with similar people whether that's ideology-based, religion-based, race-based, etc.  Trying to homogenize the human race into one culture isn't going to work.