I use the term "woke right" to describe politically correct Republicans, i.e. those who support the woke left's hobbyhorses like tearing down Confederate statues, removing Andrew Jackson on the $20 and replacing him with Harriet Tubman, and those who favor liberal immigration policies towards Third World peoples. They've absorbed the left's values systems while voting Republican, perhaps because they just want a tax cut or some particular deregulation.
That makes more sense than applying it to the nutcases on the alt.right.