What all of these movements had in common was a desire to make a society that was more attuned to justice and fairness. They wanted to do away with some of the problematic changes that had arisen during the market revolution.
In the market revolution, American society changed along with its economy. Society came to be less cohesive. Traditional bonds between people fell apart and were replaced by a much more transactional society where people dealt with one another largely on a commercial basis rather than as friends and neighbors. These movements were trying to restore older ways and to bring more justice to the society.
The utopians, for example, wanted to do away with things like private property so that people would not just see each other as people to buy from, sell to, and compete with. The women’s movement wanted to put women and men back on a more equal footing as they had been when men and women were working together on family farms. Slavery, of course, was not new, but it was an institution in which people were not really treated as humans but as commercial items. The abolitionist movement wanted to end this and to treat African Americans as real human beings.
The major connection, then, is that all of these movements wanted to bring more humanity and justice into American society to replace the solely commercial bonds that were coming to exist between people.