1) Libertarian vs. Authoritarian
2) Anti-Establishment vs. Establishment
(Coppins: The flaw in this formulation, it seems to me, is that virtually every Republican who has entered Congress over the past eight years started out on the anti-establishment end of the spectrum, and then slid—involuntarily, perhaps, but inevitably—toward the establishment end.)3) Absolutists vs. Dealmakers
4) Open/Tolerant vs. Nativist/Racist
According to Coppins, nobody on the Trump side offered this division, but it was offered by many anti-Trumpists.5) Grievance-Motivated vs. Philosophically-Motivated
I thought this last was the most interesting suggestion, a divide between "Fox News-a-holics driven by tribal grievance from people who have some kind of philosophically rooted belief system." Coppins quotes Republican strategist Liz Mair as saying,
I honestly think the split in conservatism comes more down to philosophy versus identity politics than anything. Are you opposed to things on philosophical or tribal grounds? Are you a believer of a member of our clan? (Said in the Scottish sense) ...We heard a lot of this back when Trump won the nomination, Republicans who thought their voters cared about conservative philosophy and were shocked to see how little truth there was to it.
I bet if you polled Trump primary voters and asked them what was the bigger problem—insufficiently limited government or transgender Muslim feminists being celebrated at the Oscars, a big majority would say the latter.
But I think this is generally true of conservatism as a movement. The root of it is just a sense that the world is changing in bad ways, and there no reason to expect that all conservatives would be upset about the same changes or support the same responses. This is especially true when, as in America, conservatives are drawn from all social classes.
Of course all political parties are divided. But it may be that right now the Republicans are divided in ways that critically weaken their power. Maybe they will be able to work together better than they did on their health care bill, but so far the signs for their accomplishing very much this term are not good.