Yes, they do believe that people should be free to exercise their sexual morality freely. Yes they do.
Now show me where they agree to pay out of their pocket when their sexual morality choices goes badly for them. There, they want to privatize their choices, but socialize the costs of those choices. :)
They want big government to provide freedom from the consequences in life.
I’ve always said that if a leftist attempted to physically do their mental contortions, they would break their back.