You know, that’s an interesting semantic point. They use “religion” when they mean to cast it as something threatening, and “faith” when they don’t.
You are correct. They despise religion, because to them it connotes “rules” and “judgment of behavior”, “higher authority” etc.
They have faith - in themselves, in their manipulation of truth, in their own infallibility because of their “good intentions” etc etc.
Liberalism is definitely faith-based, because how else could they continue to support the same policies that have failed throughout the entire Twentieth Century, and are still failing in many dem-controlled American cities.