That's nice, but it won't work in practice, unless your definition of "religion" is a very narrow one.
"Morality" is fundamentally meaningless unless you believe that human beings have rights that no human being can take away. That proposition, in turn, requires an agency higher than any human being or human agency to grant those rights.
(After all, you have to have an answer for "why do people have the right to x, y, and z" that's better than, "they just do".)
That higher agency is God. Freedom, in the long run, is incompatible with an atheistic society, for the simple reason that men will always set something up in place of God ... and the most tempting idol to set up is the state. If "all men" are not "endowed by their creator with certain inalienable rights," because there is no creator, then those rights will be understood to be granted by the sovereign.
And what the king grants, the king can also take away. The 100 million lives sacrificed to atheistic communism in the 20th century testify to that.
Thank you, Campion. That was very well put.