Firewall of Church and State
Jesus was Jewish, and during the era in which he lived, the center of the Jewish world was the Temple in Jerusalem where the Jews went to worship. The Jews had lived there for almost a thousand years, without too much hassle from their neighbors. The original Temple built by Solomon was destroyed by the Babylonians in 586 B.C.E. and most of the population of the city was killed. The Temple was later rebuilt.
A couple hundred years afterwards, the Jews in the city narrowly averted disaster in their encounter with the Greeks. Alexander the Great came strolling through in 332 B.C.E., and the Jews showed him that his conquest of the Mecedonian world had been prophesized in their Book of Daniel. Supposedly Alexander was so delighted to see himself referenced in the Jews' holy book that he didn't conquer Jerusalem.
In 63 B.C.E, the Romans seized control of Jerusalem, occupying the city with soldiers and subjecting its citizens to a tax to be paid to the Roman empire. This lasted until around 70 C.E., when Jerusalem was burned to the ground by the Romans in response to a Jewish revolt. During this 150 years, the religious rulers of the Jewish people in Jerusalem maintained an uneasy truce with the political and military leaders of their Roman overlords.
It was in this context that the death of Jesus occurred. Crucifixion came from the Romans, and it was the preferred form of punishment for those who committed acts of treason against the Roman empire. Scripture tells us that Jesus of Nazareth was becoming a nuisance to the Pharisees, the Jewish ruling council in Jerusalem. They saw Jesus as a threat to their established power. Since Jewish law forbade murder, the Pharisees, in an effort to get rid of him, persuaded the Romans to do their dirty work for him. The Roman governor of the region at that time, Pontius Pilate, was hesitant to kill Jesus, since he didn't seem like such a bad guy, but the Pharisees were quite insistent. And so Jesus gets the nails.
Again, this is the story according to scripture; historical accounts portray Pilate as a far less merciful individual. Was Jesus killed by the Romans for his acts of sedition or was his death prompted by his acts of heresy against the Jewish rulers? It matters little for our purposes; let's stick with the scripture version.
So the New Testament, it would seem, contains a lesson about what happens when religious leaders collude with those in political power: Jesus gets killed. Arguably, this isn't such a bad thing; after all, Jesus was supposed to die, according to all the legends. But still, even if it did redeem all of the sins of mankind, this single instance of capital punishment is one that Christians point to as one of the most cruel acts of injustice in all of history.
The moral of this story points unerringly to the importance of the doctrine of the separation of church and state. Our Pharisees (e.g. Christian leaders) and our Romans (e.g. those people on Capitol Hill) should not be consorting with one another. Otherwise, Jesus dies.
The church, like any church in the United States, should seek to lobby those in Congress about political matters, but no church should seek political power, nor should those in politics yield it to them for any reason. I don't see any problem with politicians choosing to practice any particular religion, provided it doesn't cause them to ignore the lobbying of those who belong to other faiths.
All members of a church should be allowed to vote, like in any healthy democracy; I have no strong opinion about religious leaders encouraging the members of their congregations to vote this way or that way. I'd ask that all members of any religion, while voting, choose to vote their own conscience. I do have a strong opinion, which is to say a strong aversion, to any church member whose voting preferences are all perfectly identical to what their religious leader has told them, unless this happens to be a coincidence.
(To those in the U.S.: happy tax day.)