Cringe, yes, he may be. Conservative? Maybe in the opportunist sense. At most, I think he's much closer to being libertarian and would otherwise be left leaning if the mainstream left hadn't drifted so far left. Elon really wants people to get out of the way of his view of progress. Yes, I'm sure ego is a part of that, but when is it not with anyone? I'm not even sure what Elon would be conserving other than whatever ability he has to launch cars into space or dig pointless tunnels.
A better example of a "cringe conservative" would be the My Pillow guy or even Lindsay Graham. And many would of course say Trump.