Your post mixes specific religious practices with universal axioms of civilized behavior. Public virtue relates to the later, not the former.
In other words, to answer your question, the “final authority” in a free society is natural law. Just as gravity has the power to make you fall regardless of your religion, the public safety function of government consistently exposes certain basic, universal virtues as essential to civilized life, regardless of the religious makeup of a culture.
For example, I’m sure we agree that murder is destructive to civil society and falls under the public safety function of government. But murder would never occur if life was valued as it should be. That “should” is a moral premise, yet it is inextricably connected with our laws about murder.
Those laws reflect the duty of government to promote the virtue of respecting human life by punishing with vigor those who lack that virtue. This comports both with Paul’s teaching in Romans 13 and with the Founder’s view of the Creator as the source of those unalienable individual rights the government has a duty to defend.
Public virtue is not an option. We won’t stay civilized without it. If it sometimes presents us with hard questions, well, that’s just the price we pay for trying to be civilized.
Correction:
“Public virtue is not an option.”
Should have been:
“Public virtue is not optional.”
Quite a difference, eh? My apologies for the error.
In your opinion, the axioms you think of are universal. In the opinion of the Islamists, the different axioms of Sharia law are universal. In the opinion of Communist regimes, the Marxist axioms are universal.