Jaxson2 said: "United Auto Workers, International Brotherhood of Electrical Workers, Communications Workers of America, etc. all work for different companies but have a single union. Each business has to respect the union contract. So, Broadway workers could, in fact, be one union.
Why would you think that? All companies working in the theater have a contract with the production company and/or theater. Government provided services may not, e.g., post office, garbage. The Broadway League is not the production company, but its members are."
Jaxson, I'm sorry but you have a fundamental misunderstanding of labor relations both on Broadway and in general.
First of all, the various unions you mention represent different trades or crafts, and employees in those categories collectively bargain with the employers by whom they are employed. Having one union that represents employees at multiple companies is the essence of collective bargaining. But many/most employers have many unions with which they negotiate contracts. It's no different on Broadway. You seem to think that all employees of, e.g., Ford Motor Company, are in the same union. That's very wrong. Same on Broadway. Actors are not stage hands, box office treasurers are not wardrobe people, etc. There are a number of union locals under IATSE, but there are also many that are not. What are you talking about?
Secondly, I have no idea what "All companies working in the theater have a contract with the production company and/or theater" is supposed to mean or has to do with what we are talking about. The League's members include producers and landlords. Production companies (except for institutional ones which is a different matter) are not members of the League. The League is the exclusive bargaining agent for the landlords and producers that are its members. This has nothing to do with the companies that productions engage to sell stuff and the like. I'm afraid you are quite confused.
I suggested once before that if you truly wanted to learn about this business you would ask questions rather than posting incorrect information and wait for someone like me (and Fosse, among others) to correct your errors. I still suggest that. 