This seems like a complete disaster for the independence of the non-profit sector and the integrity of church state relations. The idea that the state would have a substantial view into the financial workings (and with possible economic sanctions) of churches (not at the tax fraud margins, mind you) seems to me to a line that shouldn't be crossed. I'm a bit surprised that the reaction hasn't been more vociferous. The wall of separation is largely a terrible metaphor, but seems like a hole being blown wide open. Maybe I'm just over-blowing things.
On the theoretical side of this concern - this is why Yale maintains the position that it does NOT enjoy a tax EXEMPTION from the state, but instead (because of its explicit mention in the state constitution) exists in a state of non-taxation. The distinction being that exemptions are grants from the state and can be revoked, but a status of non-taxation has a higher standing and is not subject to legislative or (more particularly) regulatory revocation. I would think, not being a First Amendment expert, that a similar tack is taken with church status.
At the end of the day, I can't imagine this would pass any form of constitutional muster, maybe that's why critics are composed about it.