Should churches that don't perform gay marriages lose their tax-exempt status?

[Mercenary]

No.
Nor should they lose it for refusing to perform a marriage between divorced couples.
Nor should they lose it for refusing to perform it between people of different faiths.
Nor should they lose it for refusing to perform it between people living together before marriage.

Or whatever other objections they may have. While freedom of religion doesn't extend to the extent that you can actively cause harm to someone and often times doesn't extent to certain instances involving public accommodation. What marriages a church performs falls into the very definition of religious freedom. To cancel the tax-exempt status in such a case is essentially saying freedom of religion doesn't exist.

I can understand people who think they shouldn't have tax-exempt status to begin with, although I disagree with such a view. I cannot understand anyone who would actively say they should lose it on this issue though.