Organizations to which donations are tax-deductible (so-called 501(c)(3)s) — including religious organizations — aren't allowed to expressly support or oppose the election of candidates, and are limited in their lobbying for the enactment of legislation. General public education, including advocacy, is fine, but not electioneering or (too much) lobbying; if they want to do that, they need to set up arms that collect non-tax-deductible donations (so-called 501(c)(4)s, as opposed to the 501(c)(3)s).
The Court has upheld this scheme against First Amendment challenge, reasoning that tax exemptions for contributions are a form of subsidy, and the government can impose restrictions on what this subsidy is used for, so long as they are viewpoint-neutral (i.e., no electioneering would be fine, no electioneering in favor of racist candidates would not be). Of course, there are often difficulties in deciding what's forbidden express support or opposition and what's permitted education and advocacy; the IRS has new guidance on the electioneering side of the question.
In any case, Paul Caron (taxprof) passes along an interesting new controversy on this, not terribly novel legally but striking because of the speech involved: An Internet message from an evangelist that "If You Vote for Mitt Romney, You Are Voting for Satan." Talk about demonizing your opposition. In any event, an excerpt from Paul's post,
[T]oday's Washington Post item Separation of Church and State and Tax Exemptions:
Florida evangelist Bill Keller says he was making a spiritual — not political — statement when he warned the 2.4 million subscribers to his Internet prayer ministry that "if you vote for Mitt Romney, you are voting for Satan!"
But the Washington-based advocacy group Americans United for Separation of Church and State says the IRS should revoke the 501(c)(3) tax-exempt status of Bill Keller Ministries, nonetheless.
Paul points out that the evangelist's statement was indeed likely illegal (again, for a 501(c)(3) that's using tax-exempt funds).