So sorry for the slow reply on this . . .
I do not know a whole lot about the alt-right people, although I’ve met a few and spent a little time on their websites. As far as I can tell, the big issue for them is white nationalism, part of which involves an appreciation for traditional elements of European culture. So they share some ideas with traditional conservatism, but they use a vocabulary that strikes me as being foreign to it a lot of the time. For one thing, the alt-right people I’ve read have no sympathy toward Christianity; they’re either atheists, agnostics, or neo-pagans.
You could say that today’s white nationalism has antecedents in the Anglo-American nationalism of the late 19th and early 20th centuries, which was really an ideology of empire. (I talk about this a little in the course.) Today’s white nationalism, by contrast, is motivated more by fear of displacement, so there’s a different tone to it.
I hope this is at least a partial answer to your question!