A friend of mine joined a Facebook Group for stripping the Mormon Church of their tax exempt status. I asked why and she said because of political lobbying. The following is a paste of my reply which generally gives my answer to you as well.
To be consistent on that stance one would have to strip the tax exempt status of about 75% of those that are and I'd say the obvious first place to start would be w/ the Catholics not the Mormons. It is ridiculously important that churches be tax exempt, both because of the tenant of freedom of religion but more importantly as a division of church and state. Church members are fired up about paying bills for things that go against their principals as INDIVIDUALS. Make the churches themselves pay and the whole damn thing is going to explode.
As a side note because I suspect this is about Prop 8 (although I haven't looked at the group) people are taking entirely the wrong tactic there. The WORD marriage means something religious to those with the religion. And while there's plenty of evidence that the Bible could more accurately be said to say that homosexuality is not tolerated by the community and is against their customs than to say homosexuality is actually a sin (aside from the fact that all sexual activity outside marriage is sinful ((although that itself could potentially spring from their misconceptions about reproduction- they thought women were basically incubators and the sperm WERE the babies hence the spilling the seed stuff))) plenty of people still believe that it is and that by the government allowing gay MARRIAGE that what they are allowing is a uniting by GOD against God's will of two people. It really is about the word and the use of by the government (because they believe government has the power to do these things).
This movement is going to be infinitely more successful if they look instead to PRIVATIZE marriage. Marriage from a legal standpoint is two things- a license, and a contract. This is an important distinction. The contract is the traditional part of marriage legally. It is your vows, it is what is being argued about when you go to divorce court, it's why for instance a cheating spouse will get reamed in divorce court- they failed to meet their contractual obligations! Any two (or more) people can make a contract with each other to do ANYTHING that is legally permissible (you're not getting retribution from the assassin you hired enforced in court) and have it enforced in a court of law. Article I Section 10 of the Constitution protects the right of contract and states that no state shall pass law impairing the obligation of contracts. These protected contracts (aside from the social, ceremonial and religious aspects) are what marriage was for basically forever. The second part of marriages legally- the licenses are part of what I call the "Big Three"- it is one of three laws born out of racism that are having the most obvious impact in the US today. Marriage licenses basically DID NOT EXIST before 1929. The idea of asking the government for PERMISSION to get married would have seemed ABSOLUDICROUS to people before that time. But back in the 20s the government were getting their knickers all in a bunch over something truly horrifying to them- BLACK PEOPLE WERE GETTING MARRIED TO WHITE PEOPLE!!!!!! Heavens no!!! They had to DO SOMETHING about that. So like basically all licenses marriage licenses were created in order to be able to deny some licenses. It is the LICENSE that gay people cannot get today. They cannot be denied contract enforcement. But they can't use the term marriage in those contracts because marriage requires the government's permission- which they can't get. If you do away with marriage licensing and go back to marriage being a legally binding contract with a social function and possibly religious trappings (if that's your bag) attached you will end the debate. Will the churches perform marriages for gay people? No. Most won't and they shouldn't be forced to. But can they BE married? HELL YES THEY CAN. This one is easy to get the religious community in line with too. Unlike a legalization of gay marriage licenses you are not forcing them to back with their money and the force of the state something they don't believe in, and when you take that away most people are more than reasonable enough to not care about what other people do. Even better they can be appealed to by the fact that they currently are having to interject the state into a holy communion of souls by God. It is like God having to ask the US government for permission. Abhorrent!