Frankly, I can't see why there should be any restrictions on the political activities of non-profits, religous or otherwise.  The sole exception would be non profits that recieve govt money. 

Here's an email I sent to a friend of mine that is related to this topic:

Think of it this way.  Suppose I am member of
a political group.  I try to collect money and then I use it for political activities, like distributing yard signs, phone
banking, walking neighborhoods, and redonating money
to campaingns.  All of the money donated to my political group,
however, is ineligible for a tax deduction.  It's not
like giving money to the United Way or Catholic
Charities.  Ah, but I have loophole--people can claim
money given to churches (and 501 (c) (3)'s) as tax deductions.  So, I turn my political group into a fake ministry, and suddenly
donations to my political group are tax deductable.

The campaigns will probably start setting up astroturf
ministries too.  So, not only does this law
infringe on the Establishment Clause, it gives tax
incentives to turn political groups into a religious
group. 

If a 501 (c)(3) wants to voice a political opinion, they are welcome to set up a 527 arm of the organization that does so.

I'm not familiar with the specific proposal that MicahSifry cites, but I've seen quite a few like it.  If it is what I think it is, then our consideration here should be very careful to distinguish between policy-related activities (which can include lobbying, advocacy, education, etc.) and electoral activities (which refer to the election of a candidate). 

A 501(c) organization (of whatever subparagraph) is so identified because of having been granted exemption from paying income taxes.  A (c) (6), for example, would receive income from dues paid by members of a professional association and not have to pay federal income tax on those dues.  A (c) (3) not only does not have to pay income tax on the donations that it receives, but donors receive a deduction in their own income taxes because of the donation. 

The IRS has struggled with the matter of whether 501(c)(3)'s should engage in policy-related activities, including lobbying, and come down on the side of allowing it--within limits.  The idea is that charitable organizations often serve elements of the community who lack a voice in public policy and therefore are also served by advocacy by the organizations that serve them.  These organizations are the point at which, to coin a phrase, the rubber meets the road, so they are quite likely to have valuable experience with the actual effect of specific public policies on specific groups of people and can, therefore, be relied upon to provide valuable insight for policy makers regarding community needs. 

To make themselves heard in the public arena, these organizations often have to use the tactics and strategies that will, well, allow them to be heard.  They write letters to Congress.  This is lobbying.  They send out action alerts.  This is lobbying.  They stage media events.  This is not necessarily lobbying, but it often has an effect on the public policy debate. 

BUT 501(c)(3)'s are strictly prohibited from participating in electoral politics.  They don't endorse candidates.  They walk a very fine line in order to have candidate forums or issue candidate report cards.  They can engage in voter registration and can encourage people to vote (without indicating any sort of preference for candidate). 

This is something of an oversimplification, but it generally says that charitable organizations can and should engage in public policy discussions--and stay the hell away from electoral politics.  Both elements are good.  The tax exemption and the tax deduction are both forms of public support for an organization.  The prohibition against using public dollars (even public dollars that have been foregone) to influence an election is one way to avoid using your tax dollars to bring about a government which you might not support as well as eliminating improper government influence on the positions of an endorsing organization.  On the other hand, the unique and specialized experience of a charitable organization can bring value to the public policy discussion.

For example, do you know what effect the creation of a preferred drug list with a prior authorization requirement in your state's Medicaid formulary might have on people living with HIV?  Your local AIDS organization does.  And that ASO's voice in the debate is probably why HIV medications have been specifically carved out of the PDL.  That "voice" may have included letters and other contacts with policy makers, press conferences and other media events designed to call attention to an obscure (bur life threatening) issue, and testimony at hearing after hearing.  If you donated to an AIDS organization and that AIDS organization participated in this sort of discussion, then 20 cents (max--and probably a lot less) of your dollar went to save lives in just this way.

I'll check on this proposal to get more details, but it looks like an attempt to block association among organizations (an important means sharing policy information and organizing advocacy) and--more importantly--scare a few more organizations out of the public policy discussion.  It won't have a dime's worth of effect on elections because 501(c)(3)'s are already prohibited from participating in electoral politics.