Don't use the word. Ever. It is tantamount to wearing a sign around your neck that says: "Vote for me. Not only am I anally-retentive, but I enjoy using words the average person doesn't understand."
"Governance" is better, but what's really needed is a phrase that explains why "polity" is theology. A challenge to our polity is a challenge to "the way we discern and respond to the will of God."
Or words to that effect.
Update: Brian Kaylor's thoughts on this are worth reading, as always.