"God hates gays" in particular, yes, I think they would be justified in dropping the banhammer on that. Blizzard has gone out of their way to promote inclusivity and diversity with Overwatch (which has two canonically gay main characters), even though it pissed off some of their more conservative fanbase. Having people on stream coming out against that runs pretty directly counter to the politics that Blizzard has already been promoting.
What it comes down to is that I expect Blizzard to have a system of values guiding their decision on this, and I want those values to line up with mine - everyone gets human rights, democracy is preferable to authoritarianism, freedom to protest a corrupt government is an essential right, etc.
Some people would probably call it a double standard to let players support pro-democracy protests, but not support anti-gay ones. I'd just call that having standards. It's 2019 and we're talking about a game studio based in southern California.
Maybe that's a self-centered view of mine, expecting a corporation to support western values just because they're based in the US and composed almost entirely of American employees. But that's where I'm coming from.