That all depends on whether you define a Republican or accept a Republican. By definition, he's a poor Repub at best, with his huge buildup of government and fundamental disregard for the entire US Constitution. But by acceptance, since he's the primary officer in the national Repubican Party, he's 100% Republican and there's no question about it.
Either way, the Repubs can run a retarded goat that bleats "911!" over and over and over, and about 50 million registered Republicans would vote for him. Acceptance has conquered definition.
Note that the same kind of analysis applies to the Democrats. Who here really thinks Billary is a Democrat by definition? The Dems don't run definable Dems, as a rule. Instead, they run Globalists who basically lie to the public in order to get elected by 50 million fucking OTHER morons called "Democrat voters".