I think that individuals absolutely MUST allow their faith to inform and shape their politics and political involvement. Otherwise, we are merely whited sepulchers, saying one thing and doing another.
On the other hand, I think that organized (or disorganized, as the case may be
) religious bodies should NOT insert themselves into the political machinery. The role of the church, IMO, is to teach the individuals so that individuals can act (and vote) according to their conscience shaped by faith. I do not believe that the institutional church is to play a direct role in shaping government policy.
In my mind, the institutional church should say "These are the teachings of our Lord and Savior Jesus Christ. This is how these teachings have been interpreted through the centuries." It is then the responsibility of the individual Christian to look at Law X or Candidate Y or Situation Z and act accordingly. In general, I do not think that it is the proper role of the institution to support or condemn specific Laws or Candidates. On the other hand, the institution can and should denounce Situations, but I do not think they should mandate how the individual Christian responds to that Situation.
Obviously, there are going to be exceptions to what I've just said, but I think those exceptions should be extremely rare ... and extreme.