OK so you are willing to state that Disney has never sued a non-commercial entity for using their name, right?
I have provided you 3 scenarios; and tire of attempting to read your mind. How would (Disney, Six Flags, SeaWorld, Busch Gardens, Magic Mountain, et. al.) be able to sue, if they were named as the recipient of a group's gathering place? Can you cite a single example?
If 'The Hillary Rodham-Clinton fan club' wanted to use your resturant, hotel, theme-park, zoo or city park as a meeting grounds; you are prohibited by law from preventing them to do so.
However, as this is YOUR park (as in Sea World, Disney, 6 Flags, MM, et. al.), YOU can place limits on what is tolerated and what is not. For example, if you state that you have dress codes for EVERYONE, you may enforce that. Same thing for permissable behavior. Also, to the best of my knowledge, local laws would also be enforced (lewd or profane conduct would not be tolerated).
For example, there are signs at both Disney Land, and Disney World warning that pranity will not be tolerated. You can be ejected from the park for swearing.