Not at all. There is no equivalent of Elmer Gantry in their celluloid ranks. Mormons are left alone. So are Quakers, the Amish, and other pacifist groups. These groups are perceived as not having enough votes to give liberals political trouble, at least not outside of Utah.
Liberals are willing to write off Utah.
They organized a boycott. Fundamentalist pastors rarely organize local boycotts, but they had had enough. They asked their members to agree for one year not to attend any local theater that showed it. Then they approached the manager and told him that it would hurt his business to show it. He showed it anyway.