Jesus was an anarchist. I don't say this as an insult or a dig. Many people labor under false ideas of what anarchism is. Anarchism is belief in the abolition of hierarchies and the organization of society on a voluntary, cooperative basis without force or compulsion. There are different ideologies, many of which have to do with the abolition of capitalism in favor of others systems of economics such as barter systems or co-op models. This is because for many anarchists, capitalism is seen as another system of hierarchy. Additionally, many anarchists subscribe to a pacifistic philosophy, as they do not believe in compelling others to do anything. If you want a good idea of what an anarchist seeking to set up a more perfect society would look like, look to Jesus Christ.
Christ was a visionary, who preached ideas such as "Do unto others as you would have them do unto you", and "if you have done it to the least of these, my brethren, you have done it unto me." He introduced ideas of equality, empathy, and justice that would attract those most in need, and most oppressed by society. It is said that he spent his time with "sinners" such as sex workers, tax collectors, and even forgave the thief who hung next to him being crucified. Why? Because, those are the people who needed that message. The traditional messages of the existing religion, the existing social structure, and the existing political structure was failing these sinners. They were starving, they were selling their bodies to survive, and working in professions which resulted in them being shunned. Much like now, the wage economy was failing many people in the society.
Did Jesus tell them to work harder, or pull themselves up by the bootstraps? He did not. He essentially kicked Wall Street out. When he began to gain popularity, and the rich began to seek him out as a spiritual leader, he told them they must give away all their wealth to know god. Christ taught against setting one person above another, sought to abolish hierarchies, and wanted to help the Jewish people liberate themselves from further Roman oppression by "rendering unto Caesar what is Caesar's" and getting rid of their money, getting off the wage system, and giving that back to the Romans to keep from letting money control them.
Early Christians even lived in communes, living the Law of God, sharing their possessions in common after Christ's death for a time. We see Paul and some of the other Apostles try to help these spread out branches try to manage their affairs in the Epistles, but eventually their spread out nature leads to schizms and discord, and then of course Nero takes it upon himself to kill Christians, who were known to be anti-authoritarian.
Mormons later see the rise again of these communes in The Law of Consecration, in Independence, Missouri and Nauvoo, Illinois. These ideas of sharing possessions in common are fundamentally important to the faith, and in Mormonism, as well as in much of Christianity, it is understood that this is what the Kingdom of Heaven will be like.
Some of the words that Jesus is most remembered for, "if one take away thy coat, give him thy cloak also; and if one smite thee upon the one cheek, turn to him the other also?" Are also ideas that much later crop up in pacifist-anarchism. Anarchism is about having no hierarchies, and having every person be equally important (one could say in the eyes of god). Anarchism is about letting people make their own choices and not compelling them to make one choice or another. This is also a crucial part of Mormonism and of most sects of Christianity. God gave humans free will to choose, and that was why Christ came; to atone for when people made mistakes learning and figuring life out. In Mormonism, the belief is that it was Satan himself who wanted to strip people of their free will and force everyone to do the correct thing.
In Mormonism, there are Thirteen Articles of Faith. One of the most relevant to considering the political left, is: "We claim the privilege of worshiping Almighty God according to the dictates of our own conscience, and allow all men the same privilege, let them worship how, where, or what they may." Again, this goes back to the Satan versus Jesus, being compelled in all things versus self determination. In fact, the first Modern prophet of Mormonism, Joseph Smith even said, "Be ye not commanded in all things." When we look at this, it seems clear that Mormons should support people, and groups on the political spectrum who support choice, support diversity, and support healthy freedom of speech, even if those participating don't have identical values to Mormons themselves. Remember, Jesus hung out with sex workers, because he took the time to understand their needs and their lives, and because he was filled with love and empathy.