>By federal law, if a company has a union, the union must represent ALL non-management workers, even those who do not pay dues.

This is not true. There can be non-union job classes even if the employer has some unionized employees. Even in different geographic areas you can have one location have class X union and another non-union (eg Starbucks).

What you cannot do, is have a unionized location with union Software Engineer I and non-union Software Engineer I. Sometimes employers try to skirt this and have non-union jobs that are too close to union jobs, and then it's lawsuit time.