Well, no... The Left may be imposing their moral codes more successfully than some other groups. But they're hardly the only ones trying to impose morality.
Every law imposes a morality on the one who would choose to break the law.
Don't be confused by the fact that you think some moralities are universally recognized without religion. All laws distinguish "right" from "wrong." Without an absolute moral standard, all notions of "right" and "wrong" can change with time.
All of them.
Shalom.