The law in question does NOT require that anyone join a union nor pay union dues.
What it does do is say that anyone who benefits from contractual agreements won as the result of collective bargaining by a union, that that union has the right to collect from those non-union members a fee, which is already part of the dues that union members pay, which has been assessed to recover the costs associated with only the collective bargaining activities of the union. In other words, there is no such thing as a free lunch, something that should be well understood by conservatives.
As I mentioned previously, the law in question had already been ruled constitutional with a UNANIMOUS decision in 1977 by the Burger court, which was generally considered to be a conservative Supreme Court.

OCU