The assumption seems to be that conservative/ traditional religious bodies and their organizations should just roll over and take this. Could a case be made that such a move violates the First Amendment at two points? 1. It amounts to establishment of religion because the government would limit the tax exemption to religious bodies it approves of. 2. It violates the free exercise of religion by having government dictate religious belief and practice.
If not, then maybe conservative Christians, Jews, and Muslims might want to take a “hard line” against the regime. Don’t pay the tax. What is the government going to do, lock our houses of worship and jail clergy and the faithful who resist? That would make for bad visuals, but this crowd might be beyond caring about that. I hope the country is not so far gone to put up with that but, in case it is, then at least we will have obeyed God rather than man, and can trust that God will honor that.
It's a little more complicated than that. The Democrats are proposing that contributors to churches will not be able to take a deduction against their income tax for their tithes and contributions. This may hurt the income of churches.
The fact that churches are supposedly subject to taxation is a fiction created by the IRS. Even before the income tax, churches were considered to be exempt because of the First Amendment.