I believe that the crux of the IRS rule (it may just be an IRS administrative rule from the "Regs", not actually found in the USC - anyone know for sure?) is that if Religions could take their religious donations (which are tax exempt), and apply them to back political parties and nominees (versus causes or initiatives), then any political party could solicit political donations through religious organizations (or even make up a new religion or church for that purpose) and gain the advantage of tax exempt political donation whereas political donations are not currently tax exempt.
I don't think there's any moral or ethical dilemma if the US decided to make political contributions tax exempt, because you can use them as deductions in Canada and that doesn't seem to be the cause of any great societal decline in Canada. But that's the way the US does it, probably because lobbying is so prevalent and thus corporate $ would escape taxation through any tax exemption.
Anyway, I've been quite surprised by Romney's church in that they've kept a pretty even balance between political parties in spite of the memberships strong leanings towards the GOP. Right now there are over a dozen mormans between Senate and Congress including the very liberal Senate Majority Leader, Harry Pelosy (I mean Reid). For the record, Mormans have backed initiatives like the California Initiative defining Marriage which was recently struck down by the very liberal CA Supreme Court decision. The LDS Church doesn't make much fuss until society starts messing with the family.
Commenting on the employment of priests (someone above asserted that "paid priests = priestcraft"), they have to pay taxes, but their church doesn't get a deduction because they don't pay taxes. But, if men like Heller continue on the current course, they'll end up stripping their respective churches of tax exempt status. Then they can deduct the pay they give their preachers. However, of course they would lose their tax exempt status and their congregation can no longer deduct their contributions because the churches would no longer be qualified organizations on the IRS Schedule A.
I asked an agent why the IRS doesn't track churches' political activity more carefully and it's because most churches operate as individual units without centralize financial structures so if, say, a Baptist Church came under investigation, the congregation could just disband and reform under a new name. The Baptists (which are a convention) would remain relatively immune to the audit of their status because of the lack of centralized authority and financial structuring. Catholics and Mormons need to be much more careful, however, because of centralized leadership and financial structures. There's a lot at risk for both faiths.