Well, of course they have the "right" to make this video. No one is suggesting otherwise. But having the right to do something isn't the same thing as HAVING to do it.
There's freedom of speech in this country, I have the right to make a video using every offensive word, slur and stereotype there is. I can do that, it's my right. But that doesn't mean it won't be offensive to people.
And, really, we should be in an "advanced" enough society that doesn't tolerate such parodies and caricatures. I go back to my black-face reference above. If a movie was made today with white men playing black men using black face and other offensive features common to turn-of-the-(last)century performances (big, red lips, monkey/ape-like features people would call it offensive and would rightfully protest the movie.
It shouldn't be tolerated to treat a group of people in such a manner and that's how I feel about this gay-stereotype in the video. It's highly offensive and its very obviously a gay stereotype. Sure they have the right to do it, and I support that right, but that doesn't mean I'm not going to be offended by this depiction. Even if it was under the guise of the character "being a woman."