I've actually heard this profoundly silly argument a number of times on the internet:
Yesterday, Catholic League president Bill Donohue was complaining about Guinness pulling its support from the St. Patrick's Day Parade, because organizers don't allow gay groups to march with signs in the annual event. Then he said he wanted to march in the NYC Pride parade, with a banner that says, "Straight is Great."
If gay people want to march in St. Patrick's Day parade, then they should let straight people march in Pride!
Um, sure, except:
1. From what I understand, it's gay Irish people who wanted in on the St. Patrick's Day parade, so the analogue is Irish gay people having a float in Pride that says something positive about Irish-ness. Which doesn't seem like something that would stir up any controversy at all. And...
2. When have straight people been banned from Pride? The few I've been to had quite a few straight people in the parade: PFLAG, politicians, children of LGBT people, straight best friends, marketing reps from various brands....
The silliness comes from the idea, common on the right, that the left organizes in the same way the right does: top-down, well-funded, ideologically pure, and with the goal of eliminated anyone who's different.
Donohue made that asinine comment because it's the sort of asinine comment homophobes make among themselves all the time. They really (want to, at least) think that being pro-gay means being anti-straight so that they can find some reason for their hate.
Anyway, NYC's pride parade director responded that Donohue can march with them and say how proud he is to be straight if he feels like it. Maybe this will stop people from making the same bad argument, but I doubt it.