Indeed, one criterion that ought to be applied more rigorously in modern scholarly proposals about the “historical Jesus” is what we might call the condition of “crucifiability”: You ought to produce a picture of Jesus that accounts for him being crucified. Urging people to be kind to one another, or advocating a more flexible interpretation of Jewish law, or even condemning the Temple and its leadership—none of these crimes is likely to have led to crucifixion. For example, first-century Jewish historian Flavius Josephus tells of a man who prophesied against the Temple. Instead of condemning him, the governor decided that he was harmless, although somewhat deranged and annoying to the Temple priests. So, after being flogged, he was released.
This is an important point: if your “Jesus” is not one that so upset the Roman authorities that they kill him in humiliating fashion, then it is not the true historical Jesus.