OK - how about this... They do have the right to have rules... But they are subject to public pressure about those rules.
Yes. Suppose I got a huge campaign in the community to disband the existing homo club. Any bets on how fast the queer support juggernaut would be rolling into action?
My point is that there is a lot more community support for squelching the "in your face" behavior of the homos than there is for the closing of Hooters, or penalizing those who go there.
As things stand today, neither is something a public institution can meddle in. Not saying I like it; but there it is.