Union contracts with the company typically bar the company from keeping or entering contracts with non-union workers that have different terms from those of the union.
In many (23) US states, when a union forms at a workplace, it can compel all non-union workers to pay fees to the union, weather they want to join or not.
I think most US workers would be for unions if they were presented as you described, where you can choose between different options or working without a union.