Actually, yes. Abortion is a bad example, because the argument will devolve into a fight over whether a fetus is a person or not.

But let's take a simpler example: gay civil marriage. Many cultural conservatives say that allowing two men or two women to marry infringes on their rights. How? In what possible way does allowing someone else to marry affect you? Does it stop straights from marrying? Yet the opposition to Obergeffel was typically framed in terms of "this goes against my religious rights". Again, how?