That would be true if only "sexual orientation" were a protected non-discrimination category under the law as race and religion are. As far as I know there is not such federal law saying so. Is there such a state law in Florida?
This link shows that sexual orientation is protected by the Orlando City council. Disney can see the writing on the wall; they can either make waves and get sued, or they can remain silent and be punished.
On top of that, we also have the perceived Constitutional belief that 'all men are created equal'; and 'all men' includes men, women, gay men, gay women et. al.
Simply stated, Disney can not win; they can only moderate how much they lose. If they chose to fight this and ban gay organizations, they will face boycotts from Liberals and as Liberals are approximately 50% of their target audience, the boycott will hurt. Then, they can fight the ALCU in court; and get their company drug through the mud. This would likely bankrupt them.
If Disney were to chose to welcome Gays, they face a boycott from conservatives, which is the other 50%. If they say nothing, and ride it out; they get their nose rubbed in the dirt and have to put up with a Gay Outting day or two a year; then it's over for until the next year. It's a no-win situation; and EVERY theme park in the USA is a target. Sea World, 6 Flags, Magic Mountain, Islands of Adventure, Busch Gardens, Disney, Knotts Berry Farm .... everyone is a target; and there is nothing either (or all of them) can do about it.