The First Amendment has no impact on what restrictions non-government entities put on other non-government entities.

If you wish to enter my house, I may require you to start every sentence with "Waka-waka" or I may require you to convert to Pastafarianism. My house, my rules and the only thing that you can do about it is to choose not to enter. However, the First Amendment protects you from the government requiring you to say "Waka-waka" or worship the flying spaghetti monster.