With all due regard for your expertise, Phil, I am under the impression that churches have a different designation, with similar but not identical restrictions.
There is no evidence that Jesus set out a political agenda.
I think maybe there is. The Israel of Jesus' day was a theocracy, albeit under occupation by the infidels from Rome, and most of Jesus' followers believed him to be the "King of the Jews", a savior in the very temporal sense of delivering them from Roman rule. When Jesus argued Jewish law with the Pharisees, it was not merely a religious argument, it was the law of the land he was taking issue with. The woman caught in adultery, to give another example, was not being stoned to death by a group of vigilantes, rather her assailants were exercising their legal right to execute the Court's sentence for her crime.
He was all about a one-on-one individual relationship with God, wasn't he?
No, he wasn't. Jesus told his followers that no one had a direct path to the Divine. They had to go through him.