First, if Jesus was an actual historical person, and there is no actual real evidence to support this, he absolutely would have been a socialist in a modern sense. That doesn't necessarily mean communist. It can mean just a very strong social safety net.
Although, you could probably make a case that, based on his alleged teachings and what the bible and scripture said about what he said/believed, he very well could have been a communist, not a Lenin/Stalin totalitarian, but more of a true governmentless communist. He may also have been pragmatic enough to realize that would never work, and so while ideally he may have wanted that sort of society, he would know it couldn't work and would just lead to worse suffering. So yea, you'd end up with some sort of centralized governing authority overseeing a very strong social safety net. He would absolutely not support capitalism for greed sake, which is the primary motivator of capitalism. Capitalism would be a tool, if it was permitted at all under a Jesus government, to support the social safety net.
I'm not even religious, and apparently I know more about the alleged teachings and beliefs Jesus than people that will profess to be Jesus lovers.