Let's be clear--churches and believers should speak prophetically to their communities and cultures. We should be speaking to our parishioners about a follower of Jesus' role in shaping political leadership, in influencing culture, etc.
But there is no way this is a good idea. As I think has been attributed to Tony Campolo, mixing manure and ice cream might be really good for the manure, but it doesn't do much for the ice cream. I am not sure it's a good idea for churches to be tax exempt even, although all nonprofits are tax exempt, not just religious ones. Churches should be speaking on behalf of God when it comes to biblical truth and kingdom issues, but I don't believe we should endorse candidates either way. And I definitely don't think we should be connected to any one group or party. Anything that compromises the prophetic edge should be wisely considered and probably avoided altogether.