A version of this argument roiled the 2004 presidential campaign when some, though not most, Catholic bishops suggested that John Kerry and other pro-choice Catholic politicians should be denied communion because of their views on abortion.
Somewhere in my memory, I remember that one of the Catholic hierarchy who wanted to deny Communion to Kerry was the current Pope, then the number two man at the Vatican as a cardinal. In Kerry's case, they had a simpler argument; he was divorced from his first wife and had not undergone the sham of a Catholic annulment of that marriage.
That being said—All these churches need to back out of politics if they wish to maintain their tax exempt status. Paying taxes is what gives voters and organizations the right to participate in the electoral process. If you maintain saving men's souls is your job, then get to it, and stop throwing your monkey wrench of your single-issue political views. Why the Catholics are more concerned about the aborting of fertilized eggs over the needless killing of over a million living breathing Iraqis is something that I will NEVER understand. This is just one of the reasons that the ball-and-chain and I don't attend church services together.