Actually, as a private organization, it would be up to them to decide whether to disallow openly gay players and / or owners. Perspective owners and players would need to know of such a rule (and fans would want to know about it, too). Those who don't agree with such a stance would be free to not participate in nor support such an organization. No one's legal rights would be trampled.
As per homosexual players, I think their teammates should have the strongest word, considering that most locker rooms don't have private showers. Personally, I choose which teams to support based on performance on the field and moral conduct of its owners and players. I don't take into account sexual orientation, but will note if the owner cheats on a spouse.
That is insane. If you could do that, you could do the same to people of religion (or lack of it).
Look at the Boy Scouts of America. They are a private organization who up until recently denied both boys and leaders who were openly gay. Opening up their organization to openly gay boys (but still denying openly gay leaders) was their own decision and not the result of a lawsuit (or threat thereof). The biggest sponsor of the Boy Scouts of America is The Church of Jesus Christ of Latter-day Saints. Nearly every congregation of the LDS Church has a scout troop. The scout master of each of these congregation-based troops is LDS, but boys of all religious persuasions are welcome. The oath to be "morally clean" doesn't limit itself to any particular faith.
Now look to both presidential campaigns by Mitt Romney. Mitt Romney's family joined the LDS Church in the 1830s. His adversaries constantly called into question his Mormon faith. Huckabee even said that no true Christian could ever vote for a Mormon President. If people judge a candidate based on religion, why not judge corporations?
The main point I wanted to make is that individuals, and not the state, should be free to judge by whatever standard they want. Support organizations with values with which you agree while withholding support from those with which you disagree.