Churches, or any organization claiming IRS-approved Tax Exempt status that desires to engage in politicking should refuse the exemption. After all, they’ve acquired a benefit (tax exemption) for a restriction. Seems like a fair trade to me and easily undone if they don’t agree. Consult the IRS Guide for Churches if that is unclear.
Individuals and corporations who are subject to taxation are free to engage in such activities; clearly many do. Thus the argument by religious-themed institutions that they are being “muzzled” is disingenuous at best. In order to freely express themselves (subject to libel/ slander/ defamation laws) they just need to refuse exempt status, file full tax returns and pay taxes on profits (and unallowed expenses such as excessive pay packages).
In fact it may be time for all such non-profit organizations to pay taxes on profits. Organizations could keep their IRS designations (501[c]3 etc.) which allows contributions (to a certain level) to be tax-deductible for people and ‘for profit’ organizations. Then allow each non-profit to set aside an amount of profits (perhaps to 10% of total income) as exempt from tax if retained by the group for future use.
All income above that should be taxed if not used for eligible purposes; such as providing assistance, education & training. And reasonable related expenses; subject to similar IRS tests of reasonableness as ‘for profit’ businesses. Not only will this put such groups more in-line with individuals and ‘for profit’ organizations; it might just cover the cost of providing Universal Health Care – certainly a very worthy result.