The issue is being licensed to perform marriages. People think of that as a "perk," but really it's more of a duty to operate within certain parameters. No church that does not license marriages or open its doors for non-denominational marriage ceremonies could be forced to marry gay couples.
If you do perform those services on behalf of the U.S. government - which you are, and NOT in your capacity as a religious organization - then you are of course expected to comply with the law, including non-discrimination. That's not unreasonable.
Whether churches should maintain tax-exempt status is a bit of an open question; that status is designed to protect them as a RELIGION, not as a political entity, and it's not clear that it should (or does, although no one is going to [legally] call them on it) protect their operation in the political realm. It's a bit of a Wild West situation when it comes to how religions are currently allowed to operate and the scope of activity they can perform outside normal regulations.
The idea, the initial idea, behind tax exemption is that you can't place a financial "gate" to religions. But does that really make sense? You don't need a church to be Christian. You practice that wherever you are, and any Christian community of any size can collectively afford to raise a church even if it means doing so with their own labor, it doesn't have to be fancy. Basically, taking away tax exemption wouldn't stop any religion from flourishing (might slow growth, granted) but it would stop some "questionable" uses of religion that seem to enter the political or economic spheres.
As far as marriage equality, try to look at it with secular eyes. There are already tons of things you cannot do even if your religion mandates it, or things you have to do even if your religion mandates that you do not. The laws are in some sense written with "space" for Christianity, but if you had a religion that mandated, say, the killing of pagans as Christianity once did, you couldn't follow it, nor could you have a religion that mandated you never submit to non-religious authority like the police.
Sometimes special codes of behavior are given special exemptions (Sikhs and weapon policies for instance) but those are case-by-case. It's not clear that being able to license marriage needs such an exemption. You can still perform holy matrimony or an equivalent with no license or government recognition at all.