Some might argue that we haven't handed morality over to the government, but that we are no longer allowing one single influence to dominate the discussion concerning morality.
Not everyone in America agrees that the Christians get everything right when it comes to social mores and morality...heck, not everyone in Christianity can agree on those things.
There are things in our secular society that are secular for a reason...and are best kept that way.
No one knows better than a Christian that people aren't perfect and that we're all "hypocrites" in one way or another. However, whether everyone else likes it or not, our social mores and laws based on Judeo-Christian principles worked well for 200 years or so - in general, and not discounting the aforementioned hypocrisy endemic to Mankind. It's the past 40 years or so when we've been told that those principles were "passe" or "judgmental" or, nowadays, "bigoted," "(insert brand name here)-phobic," or "racist" that our society has seemed to accelerate its fall into madness.
Back in the 50s, Robert A. Heinlein developed a timeline for what he called his "Future History" series. If I recall correctly, the timeline had in it a block noted as "The Crazy Years" and while he didn't - that I recall - write any stories in that time block, he did reference some headlines typical of those years. While imaginative in ways I will never be, even Heinlein couldn't match the "crazy" in today's headlines.