That's funny. Why not? Your subsequent argument invokes the establishment clause in the First, which says only that a state religion may not be established.
Religion as it evolved is itself a compendium of observed realities, and the social codes espoused by religion usually assert social optimality by empirical observation of their success. In other words, religion itself is "ethics based on reality". Religion merely ascribes to such realities an underlying causality, namely an abstraction known as "god".
The Constitution poses no obstruction to laws based on religious morality; it is, in fact, a document based on religious morality. The exclusion clause merely provides that the religious basis cannot be monotone.
The Enlightenment never asserted that religion was "wrong"; merely that it had been ossified and diverted from seeking natural truths. Areligious empiricism may be acceptable, and even create stable societies. But who is to say that such empiricism has not simply discovered "God's laws"?
When you remove all non-reality based -- mystical elements-- from a religion, what would remain in that religion's philosohy?
It would be a swiss cheese philosophy full of holes.