So I can see how you could interpret it as racist and sexist ("why doesn't this woman of color support a woman of color", though that's not exactly what he said, he said a woman, or a person of color, so it could be racist OR sexist by your argument, or both), but how is it homophobic? Real question.
The reason people are sensitive is because the words get overused. I'd rather they get overused than underused, but overusing them waters down their real meaning. There are people truly victimizing and hating other races, genders, sexual orientations, etc, it really is still a problem. But if you call anything even vaguely resembling a lack of total understanding and acceptance in every way the same thing as aggressive bigotry, then a huge swath of people who don't yet have a total understanding and acceptance, but are on their way, are turned off to the whole idea and start to side with people saying that liberals are crazy and there isn't really a problem.
I stand by my assertion that Andy isn't being racist or sexist (or homophobic) with this post. He's just being an idiot. In fact I would wager he is specifically trying to rail against the very things you say he is being, but he's showing a lack of understanding and he's falling in with the mob mentality of identity politics instead.
I think identity politics is a natural outcome of the place we find ourselves in, where society is attempting to really address underlying inequalities. But it's still important to see the ways in which it damages the narrative and critical thinking of the public. Choosing a candidate based on group identity is a dangerous standpoint to make, but it can be made based on an oversensitivity to bigotry/racism/sexism/etc as well as based on actual bigoted beliefs.
