And they will go out of their way to state emphatically that they STILL ARE a family place. Six Flags has church groups go through, they have school tours, they even have corporate sponsor nights. However, if a group of undesireables decides to descend upon the public park; there is NOTHING that they can do. They CAN control the behavior of the undesireables (no nudity, drunken behavior, line cutting, abuse, ect). They may prevent a 'parade' of the groups; and will monitor how the group conducts themselves.
Freedom of association means that any group may go to any public place, with or without warning. I sincely doubt you will find Six Flags advertizing Gay Day on their website, on a road sign, or even at the front gate. This is a gathering promoted and set up by various Gay organizations. Six Flags just happens to be the unfortunate target. Given a choice, I'm certain that Six Flags would just as soon pass on the extra ticket sales for that day, and have a usual day; as frankly, this type of thing does not boost the image Six Flags works so hard to present to the public.
I understand the dilemma. I wonder if they might be well-advised to post a sign at the ticket sales counters that there is a NON-Six Flags sponsored "Gay Day" September 18th and that way ticket buyers could THEN decide whether to go in or not. That way, "buyer beware" notice had been given.