Yes, it can. The Boy Scouts hold gatherings on public property. But they can exclude gays from their membership. It cuts both ways - that also means that gays can exclude groups that they do not want at their gathering.
You are inncorrect with regard to this situation. This was a public street and no permit was required. This area encompassed businesses and homes. It was open to all and the sodomite group was unable to exclude anyone from the public street.
If the scene was different, you would be correct. If the sodomites had rented a building or obtained permission to use an area for themselves, they would have the ability to exclude people. Thia setting was not like that.