"Ain't goin down on Brokeback Mountain" is full of typical country wordplay.
The question is: who's it making fun of? The words directly ridicule homosexuals and end with an admonishment that "that ain't right."
So it jokingly reinforces homophobia.
I've heard claims that it makes fun of homophobia, but I've been presented with no evidence for that beyond wishful thinking.
Anybody who's been a redneck knows that saying something in a joking manner is often used as a safe way of telling the truth, because it can always be followed by an, "I was just joshin" disclaimer. With this song, we don't even get that.