^^ I think there is a kernel of truth to that.
In my opinion, liberals also use religion for promoting their values in the public sphere. Otherwise there wouldn't have been an abolition moment or MLK's civil rights movement, which were always couched in the theme of Christian justice. The Episcopalian service I attended last week had a sermon that was openly pro-LGBQT civil rights. The Episcopalians are generally from a liberal Protestant tradition.
The left is not as effective as the right at mobilizing religious values -- and liberals are now losing elections we used to routinely win in the upper Midwest and Appalachia because there is a vocal minority in the Democratic party that paints religious people as irrational dupes and paints religion itself as fundamentally harmful or evil. That is a message that is hard to sell in places that tend to be economically left-of-center, but culturally traditional and right-of-center, like the Midwest and Appalachia.
