It's exactly the opposite. What you call "multiculturalism" is ethnic balkanization, and that is built intentionally by authoritarian states. Not the other way around.

And yes, those moral traditions will tend to re-emerge in a society that protects the basic tenets of Liberalism based on a Christian moral order. This is mostly because any member of any ethnic group that can't co-exist within a Liberal order will have to leave or be forced to leave, because Liberalism is unwilling to tolerate other systems.

A Liberal framework, begets a liberal population (as in, a liberty-focused population based on local communal and family ties).