GOP definitely pushes identity politics, just the identies they claim to represent are frequently not actually oppressed or are the majority:

Some tropes:

* "Real" rural Americans vs city dwellers

* Oppressed Christians vs atheists and Muslims (despite both being a tiny minority nationally vs the majority Christians)

* blacks and Hispanics vs their majority white base

* College educated vs uneducated (somehow ignoring the party elite and backers frequently have elite educations)

* Gun owners vs everyone else

I cynically believe many people, including the GOP national leadership, realize these are much more manufactured than oppression faced by actual opressed minority groups. But stirring up culture wars provides a great smoke screen for their agenda while fracturing socially or racially what would otherwise be natural opposition to their policies among class lines.

See: GOP rallying the rural poor and elderly against ACA, despite the two groups being some of the biggest groups on Medicare/caid