First of all courts for years have held that these fees are okay because without paying these fees non-members are "free riders" and get collective bargaining for free.
In this ruling the court countered what they established in Citizens United. Coporations can contribute money to political causes (not campaigns or parties) in unlimited amounts with no regard for shareholders' concerns OR (not pointed out in the NPR piece) taxpayers' concerns for corporations receiving tax incentives like Walmart not paying property tax as part of their business model. Unions, after this ruling, can't contribute money to political causes (not campaigns or parties) because of the concerns of non-union members.
The kicker is that in Citizens United the court went beyond the case to state that the contributions do not have to disclosed. In this case the court went beyond to say that there has to be an "opt in" (not an "opt out" which was not part of the case. Breyer apparently gave an oral dissent today railing the court for adding on to this ruling when the parties had not been able to air their side.
What this signals is that this court is so partisan and out of control that Scalia is willing to rule against himself in Raich v. Gonzales and overturn Obamacare.