Economically, I would say closer to communist. However, he was also bigoted, vindictive and believed in eternal torture, and also hated divorce. So I wouldn't call him all that radically left-wing either.
The eternal torture thing was added in later when the second advent failed to materialize. The divine justice thing is more a platonic ideal than one of Jesus.
Most early Christians were universalist but didn't acknowledge an afterlife. That stuff materialized 200+ CE.
I'm pretty sure the gospel translations we have today are include some significant edits, with all the others derived from Mark. What I don't know is if mentions of Hell or Hellfire as an afterlife torture program are from the first century as I am not a biblical scholar. The common feared fate was gehenna, the garbage dumpsite where refuse was burned, including the bodies of the poor, outcasts and criminals.
I wrote a blog cataloguing Hell in 2016. I've been told Limbo was never a part of it though George Carlin was taught about Limbo when he was in parochial school, so there's a lot of misinformation and changing opinions within ecclesiastic scholarship.
But I also don't know if there was a definite period in which spiritual interpretations were added in. The scholarly consensus is that the apostles expected the world to end within their lifetime, and Jesus would return to collect them all and sort everyone out. They would not need to die to see their eternal life, which was literal.
But that didn't happen. In fact, Christian history teems with apocalyptic disappointments.
Not to mention he probably had more in common with televangelist faith healers. I wouldn’t be too bothered if someone insisted he was actually loaded; or was at least living the high life.
He was bigoted against the Caananite woman in Matthew 15.
He was vindictive against the fig tree that did not bear fruit out of season in Mark 11.
He condemns all non believers to eternal torture in John 3:18 specifically.
So no. He was not a socialist liberal. And the fact that you have to be told this by an atheist Jew says something about the propaganda you've been fed.