In response to Softlaw1's comment:
MLB is a closed shop.
Actually, this isn't true. From the legal dictionary, a closed shop is
A shop in which persons are required to join a particular union as a precondition to employment and to remain union members for the duration of their employment.
Players are drafted before they join the union. In fact, when they are in the minors, they aren't union members. They can't join the the union until they're in the majors, hence the name, "MAJOR LEAGUE Players Association."
And players don't have to join. Of course, if they don't join, they don't get certain benefits that are gained through the union. They still can get their pension, but they don't get royalties, for example, from merchandise sales that are distrubuted through the union.
Of course, players do join the union, but that still doesn't make it a closed shop.
Remember, after the lockout in 1994, players who crossed the line weren't allowed to join the union, yet they still played in the majors.