I would think requiring proof of vaccination will be a requirement. It's the same principle as requiring masks. Theaters are private companies. I can't see why it would not be legal. Of course, red states like Florida, the Dakotas, and others won't do it for the theaters in their states, but that's their choice. Even with the availabilty of vaccines, it may take years (if ever) to convince 90% of the population to be vaccinated, which is what is needed to create herd immunity. I can't imagine Cuomo allowing Broadway to open unless it's absolutely safe.