Legalizing prostitution and drugs wouldn't affect your religious beliefs either, but that's not the point. The author wants you to consider the consequences of state-recognized gay marriage on your religious liberties, not on your religious beliefs.
If your religious beliefs are opposed to gay marriage and the state forces you to recognize gay marriage, what effect will that have on how you practice your beliefs? Maybe none in your case. But others who provide public services to and recognize only traditional marriages may be forced to provide those same services to gay married couples against their will/judgment/beliefs.
Ok