I'm not sure it was. It certainly was if he was talking about most conservative voters. But if he's talking about the Republican party and the policies of conservative lawmakers then his statement is at least defensible. I can't get in his head so I don't know what he meant.
But I could show dozens of example of conservative lawmakers attempting to limit access to voting for certain segments of the population. And the last few Republican presidential victories haven't won the popular vote or were decided by SCOTUS.
So yes, most conservative voters are ardently pro-democracy, but the policies and practices of that side of the isle certainly suggest that their leaders don't care much for it in practice.