Church and State: Seeking Uncivil Union?

In a post today regarding the recent Pew poll that shows American opinions regarding Democrats, Republicans and religion, Sarah Posner closes with:

Another issue here is transparency. Churches can lobby, as long as it comprises an insubstantial percentage of their overall activities (but the Internal Revenue Service has never defined what that is). Churches are, however, exempt from the Lobbying Disclosure Act which requires other lobbyists, corporate and otherwise, to file quarterly reports showing how much they spent on lobbying and what laws they lobbied for and against.

Churches get all sorts of benefits from their status, including the tax exemption and an exemption from transparency in both lobbying and generally (unlike other non-profits, they do not have to file publicly available tax returns). This is because politicians are friendly to organized religion, and give them breaks other organizations do not enjoy. But if churches are going to pressure legislators to shape legislation to their will, it seems like there is an even greater, not lesser, need for lobbying transparency: the Establishment Clause. If churches are permitting to lobby, the public should at least have the right to see how they're going about it. That's not about being "friendly" or "unfriendly." It's about being transparent and accountable to the public.