This is not necessarily true. Actually, most workers, 87.5% to be exact, do not "have" unions. Furthermore, it is possible that other organizational forms - anything from professional associations to civic associations or social movements - may have a broader effect i.e. on a larger share of the employed population than the US unions do.
To avoid any misunderstandings, I am firmly pro union and pro-organized labor. The reason I posted this question was to collectively come with some good arguments that can be used to counter the relentless right-wing attacks on the remaining Left institutions. Avoiding such questions and telling people to toe-in the party line because there is no alternative does not strike me as a winning strategy.
Wojtek