People can most certainly believe in a collective moral code that is, at times, at odds with the laws of their country, and simultaneously not dictated by a central religious authority.

Desiring the state to more closely model one's personal moral code isn't a signifier that people are placing the state at the "moral center", it's an indicator that they want those with a monopoly on violence to act in accord with what they believe is right.

I do believe the collective moral codes are drifting from those dictated by religions, but I hardly think that is a bad thing, given the rigidity and absolutism of many religions.