I think it depends what you mean by "moderate". But Trump isn't big on the usual sorts of things that self-consciously define conservatism. I've known people to self-describe as very conservative because they're really socially conservative and super-opposed to abortion, etc. I've known people who would self-identify that way because they're basically libertarians who want to bomb other countries. But I'd guess that by the numbers "very conservative"s are very socially conservative.
One thing to keep in mind is that in general moderates are not as politically aware as other voters. They often describe this way because they just don't have a great handle on what they themselves stand for or what the parties stand for. They don't see themselves as having an ideology. But they're white. They're ready to believe that ISIS is a huge problem, that illegal immigration is a huge problem, and they're suspicious of politicians who are going out of their way to appeal to black people.
So over Christmas my mom, who is not a very political person but who generally votes for Democrats, is pro-choice, pro- gay marriage, etc., starts talking about how Trump is saying what everybody's thinking. Basically for her this was about being worried about ISIS - her concept of how threatening terrorism is relative to things like car accidents is shaped by media coverage. More generally there's just this vague sense that really things should be better than they are and nobody's doing anything about it, so Trump's winning/dealmaker shtick is appealing, and it helps that he's blaming someone new insofar as it's not just this hard-to-adjudicate "It's the Republicans' fault!" "No it's the Democrats' fault!"
