Drudge has always been a bit of an outlier, a guy that marches to the beat of his own drum. I don’t think I would describe him as “consistently conservative.” But I do think he doesn’t like Trump and certain of the people in his administration, like Pence.
Drudge is gay. Trump is not a follower of the LGwhatever movement. He and his advisors want a heterosexual military. That’s enough to set Drudge against him.