No you are not. You can close your business any time you choose to without explaining to anyone why you chose to close.
Many hotels close for black spring break rather than rent rooms to the thugs who inevitably act out on that week.
Since this event is timed to coincide with another larger event it would be simple to close the park for maintenance until the perverts leave. One weekend lost revenue versus permanently lost reputation.
I'll not attend another six flags park again. They've proven to be just as perverted and family hostile as disney. They don't deserve my dollars
Ok, let's be intellectually honest. First, the park plans on a daily attendance of up to ~250,000 guests. Do you have any idea how much money it takes to maintain a staff of 30,000 cast members? Let's assume the park is 100% paid for, and maintence, utilities, insurance and general upkeep costs are zero. We are talking about over $2.7 Million/day in payroll alone (30,000 employees, 10 hrs of park operation, average pay of $9/hr; assuming NO benefits, vacation, sick or holiday pay).
Now, supposing Disney does close the park on a 'Gay Day' .... the group will simply re-schedule. So, what have you accomplished? By closing, you have alienated 90+% of your target demographic; ruined a good share of family vacations that have been planned for months, if not years. You have lost Millions in revenue, and unless you want to bankrupt yourself, you will eventually miss a 'scheduled' Gay Day. Either way, you can't stop them.