A modest proposal

For Abortion Foes, a Victory in Health Care Vote
By DAVID D. KIRKPATRICK and ROBERT PEAR
Published: November 8, 2009
NYT
WASHINGTON — A restriction on abortion coverage, added late Saturday to the health care bill passed by the House, has energized abortion opponents with their biggest victory in years — emboldening them for a pitched battle in the Senate.
...
Both sides credited a forceful lobbying effort by Roman Catholic bishops with the success of the provision, inserted in the bill under pressure from conservative Democrats.
[emphasis added]

Tricky issues at play here: First Amendment's separation clause meets First Amendment's freedom of speech provisions.

I believe I have the knife that will cut this Gordian knot.
Abolish tax-exemptions for religious organizations. All exemptions, all religious organizations.

In my naive reading, "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof..." means what is says. Congress shall make NO LAW respecting an ESTABLISHMENT of religion.
As it stands, the Government, with its tax-exemptions for religious organizations, plays umpire in the game of "Are you a church?" SCOTUS has gotten involved. By granting tax-exemption to what the government recognizes as "religious organizations", Congress implicity establishes these as legitimate religions. The Church of Joe the Plumber likely will NOT be granted an exemption - and is thereby dis-established by the government.

In return, religious organizations, like any other legal 'person' - individual, partnership, corporation - will be free to engage in political speech to their hearts' contents, with no strings attached.

Of course, donations to religious organizations would no longer be tax-deductible.

This could probably be drafted in a fairly short paragraph. "Sections X, Y, and Z of the United States Tax Code are hereby amended. No church, synagogue, mosque, coven, cell, convent, friary, etc., shall be granted a tax-exemption. All income deriving to any such, whether as an individual or a corporation, shall be subject to the relevant tax rates stipulated in the United States Tax Code. Furthermore, no donations to said organizations shall henceforth be eligible for a deduction under section Q of this code."

See how easy it is!

p.s. Here's just one example of the Government's ability to effectively "establish" an organization as a religious entity - or not - based wholly on tax-code interpretation:

In 1967, the IRS stripped all US-based Scientology entities of their tax exemption, declaring Scientology's activities were commercial and operated for the benefit of Hubbard. ... The case was eventually settled in 1993, at which time the church paid $12.5 million to the IRS—greatly less than IRS had initially demanded — and the IRS recognized the church as a tax-exempt nonprofit organization. ... Scientology cites its tax exemption as proof the United States government accepts it as a religion.
[Wikipedia article, Church of Scientology; emphasis added]

If nothing else, keeping such cases out of court would save us a lot of hard-earned tax $$$!