Yes, he does.
That article makes it clear that he is still a leftist, and an extreme one at that.
He only objects to two things:
1) His friends are "going too fast".
2) They might hurt Israel.
Those two things don't make you a conservative.
Klavan is doing what he said he rejects: Making a moral framework of accepting homosexuality because he has gay friends who he cares about. IT is too tiresome to (re)explain how it is possible to love your fellow man without condoning immoral acts. But maybe that is what some of us are called to do.