I've seen this argument around a bit and I don't entirely agree with it, though I certainly agree with a lot of what you're saying. You seemed like you would be interested in differing opinions, if not never mind.

Anyway. I think the kind of behaviour you're talking about exists, and it's hypocritical and complicit with the injustice it claims to be fighting. No disagreement there.

But. While SOME people who make a big song and dance about social justice behave this way, not everyone does, and while Forgive me for being a little suspicious of anyone who goes on and on about the need for diversity, but makes excuses to not watch shows that actually are diverse is entirely reasonable, I think I've taken to avoiding fans who scream loudest about social justice can easily become an excuse to avoid people who are making valid criticisms you don't like just because they're expressing themselves strongly. Why not just avoid the hypocritical ones?

Perhaps we've just encountered different sorts of people! The people on my flist/reading circle who talk the most about social justice do not seem at all correlated with the ones most interested in Sherlock, Supernatural etc (though there is some overlap), their (and my) response to such shows is generally to check it out because everyone's going on about it, post once or twice in annoyance about it's sexism etc and then stop watching. Or if we do like faily stuff (because most things are somewhat faily in one way or another) we'll write femslash or picspams of the non-white/POC characters etc. Or if they(*) are in love with the archetypical Two White Guys (you can't entirely help who you squee over) they don't pretend this is because the alternatives suck. To point to one of your specific examples, despite having a LOT of very vocal social justice type people on my flist, many of whom like Dr Who, the only times I've encountered anti River Song rants has been via friends complaining about them.

I mean noone is perfect, everyone with strong ethical opinions is likely to be a little hypocritical about them from time to time. But I don't think people who complain about sexism etc are any more prone to this than anyone else, and it feels counterproductive to only support criticism of popular culture if it's sufficiently polite or whatever.

(*)I am not generally a big fan of Two White Guys shows myself. But I do like stuff like Castle etc, which are nearly as bad.