I just think it is inaccurate to call that leftism. There are certainly leftist in the US and there are also similarities between socialism and social liberalis

I just think it is inaccurate to call that leftism. There are certainly leftist in the US and there are also similarities between socialism and social liberalism, but the game being played in the US isn't a leftist one. It isn't about state intervention, union power or even legislation. That private individuals, institutions or companies should be able to do and say whatever they want is even a right wing positions in the first place. Just that it originally was about teaching about god, excluding gay people and firing union organizers. So if anything, people that want precedence for their opinions are right of liberal and not left. The left position is that important institution shouldn't be private (or at least not privately funded) in the first place and/or primarily be accountable to the state rather than individuals.