I'd ignore the causality and credit-for-popularity aspect and go "what in fuck makes you think 'live and let live' is postmodern, rather than classically liberal

This is partly what I did say, and as mentioned, they think it can be both, and postmodernism is responsible for more recent changes. They also seem to be associating moral relativism with postmodernism.

It doesn't seem so far out to agree that postmodernism has this concept; a Google search for "postmodernism live and let live" has several books saying it's a postmodernism ideal.

Postmodernism involves a new kind of tolerance for learning to live and let live.

From the third result (for me at least).

I don't think I'll win this particular debate by misdirection.

What does it mean for a concept to be responsible for a change in society?

For a complete but not very useful answer, "the counterfactual in which postmodernist philosophy never came into being has less acceptance of those concepts". Or "there's a causal link from postmodernism to a substantial portion of the population accepting such concepts".

I'm not really sure of predictions to make; that's why I'm asking. Maybe polls would show a correlate between belief in specific ideas unique to postmodernism and " live and let live" (or proxies thereof)?