I agree that identity politics is not unique to the Democratic party. To a point, we all engage in identity politics in our everyday lives. I do think that a decent portion of the identity politics we see in the Republican party is the result of, and reaction to, identity politics in the Democratic party...but that a different discussion.
"Woke", at least on the right, is a cover-all term for most anything related to social activism that the Republican party doesn't like. Trans activism, DEI, progressive legal concepts....you can throw affirmative action in there. To varying degrees, those things are interwoven with identity politics and seem to be what voters are pushing back against.