Hi, Kennem! Thanks for pointing me in that direction. The law still doesn't seem all that clear, to me, though. For example, this quote from the IRS's "Tax Guide for Churches and Religious Organizations":
"In general, no organization, including a church, may qualify for IRC section 501(c)(3) status if a substantial part of its activities is attempting to influence legislation (commonly known as lobbying). An IRC section 501(c)(3) organization may engage in some lobbying, but too much lobbying activity risks loss of tax-exempt status.
Legislation includes action by Congress, any state legislature, any local council, or similar governing body, with respect to acts, bills, resolutions, or similar items (such as legislative confirmation of appointive offices), or by the public in a referendum, ballot initiative, constitutional amendment, or similar procedure. It does not include actions by executive, judicial, or administrative bodies.
A church or religious organization will be regarded as attempting to influence legislation if it contacts, or urges the public to contact, members or employees of a legislative body for the purpose of proposing, supporting, or opposing legislation, or if the organization advocates the adoption or rejection of legislation."
So I think it needs clarification. And I absolutely support the free-speech right of churches, but don't see why revoking their tax-exempt status for breaking the rules for tax-exempt organizations constitutes restricting their free-speech rights any more than prohibiting them from supporting candidates does.