Jesus announced the arrival of the Kingdom of God - what could be more "political" than that? Let's be clear: despite widespread misunderstanding about this, Jesus is indeed claiming to be a king over this present world, not a mysterious unseen world of interior "spirituality".
During the enlightenment - and all us westerners have been deeply influenced by it whether we acknowledge it or not - "religion" and "politics" were split apart. The New Testament knows nothing of such a distinction - it is something we have imposed on the Scriptures and done great violence to them in the process.
Having said this, I think we agree that we (Christians) are certainly not to conform to the kind of politics that we, sadly, see much of. But we are not to withdraw from the public square and concede the fight to other forces.
You are wrong about there being no division between politics and Religion.
Before Macchabean times there was a High Priest as well as a King in Israel. In Exile, there was an Exilarch and a High Priest. There was always a division between the secular power and the Religious one. This only ended when the Maccabees usurped the Kingship after the war with the Seleucids, but was reintstated by the Romans when they made Herod king.
In Jesus' time we have the secular Roman Authorities supported by the Jewish high Priest with a legal division between cases that could be seen by the Romans and purely religious Jewish questions seen by the Sanhedrin.
The Romans also had a division between the Priestly colleges and the Elected magistrates in Republican times, although sometimes they were the same people. The laws and electorate between the two were vastly different with certain religious roles only filled by Patricians.
This continued after the Empire became Christian with a system of Officials on the one hand and Bishops on the other.
There has always been canon law and secular law, dukes and bishops, the King and the Church. Sometimes they impinge on each others territory, but there is a division.
The Enlightenment has nothing to do with separating church and state as certain countries never did that, such as Britain. Politics and Religion were already discussed separately by Aristotle. You are very much mistaken on your facts here.
As to the New Testament, the Gospel of John says explicitly that His Kingdom was not of this world (John 18:36), hence Pontius Pilate sees Him as innocent of insurrection (the punishment of which was crucifixion). It couldn't be made more clear that Jesus was not referring to our secular world. Afterall, He tells us to turn the other cheek and no Politician or Monarch who tried that would survive very long.
We imposed no division on the Bible, it has been present since Aaron and Moses; Samuel and Saul etc etc.
I agree that Christians shouldn't withdraw from politics as I had alluded to in my previous post, as we would be immoral if we didn't act against the iniquities of the world, but this world will pass to nothingness. Politics should always be a secondary concern to your Religious well being.