Doesn't seem any crazier than voting straight down a party line, which plenty of folks here do, if I recall correctly. Seems pretty reasonable, my only concern would be if their tax free status was used to power a campaigning platform. Seems like a conflict of interest that way. Same if federal funds (ala, 'faith based initiative' money) were used.
But as community centers of like minded people... Why should they be restricted? This doesn't look like direct church control of government, just looks like awareness and use of the democratic system, the same thing anyone can do.