You have provided us with the best definition of Shria Law, Christen style, now haven't you?
As I pointed out in earlier posts, the natural rights theory was outlined by the Catholic philosopher Thomas Aquinas, who was influenced by both Scripture and Aristotle, and developed by Protestant legal theorists in the 17th and 18th Centuries like Grotius, Locke, and Blackstone, who were the principal influences on the political philosophy of the Founding Fathers. The fact that this natural rights theory was accepted by the Founders, Christian or not, did not cause them to abandon English common law with respect to various forms of sexual misconduct. By and large, these laws remained on the books in all states until 1960. If the underlying principles of American government until about 45 years ago were the same as sharia law, then the implication is that all 50 states were authoritarian theocracies for most of our country's history.
As for the red herring you introduced about judgment and sharia law, perhaps a review of the definition of judgment is in order, in this case from Merriam Webster's Online Dictionary: "a formal utterance of an authoritative opinion b : an opinion so pronounced". Utterance of an authoritative opinion is not an exclusive role of government. Until recently, Bill Gates' opinion was authoritative in Microsoft. Pope Benedict XVI is clearly authoritative in Roman Catholicism. Einstein's scientific opinions have been authoritative among physicists. Microsoft, the Catholic Church, and the physicist community are not governments, yet they have had persons who speak authortiatively.
With regard to the Biblical citation, the judgment of the believers, as cited in Acts 17 or I Corinthians 6, have nothing to do with the civil government. The authority of the church, with respect to "binding and loosing" or church discipline, is within the body of believers and not the entire world. A church may fire a pastor or expel a member, just as a company may fire a CEO or an employee, but that has nothing to do with civil government. The "sword" of the magistrate in Romans 13 were made in the context, not of a government of Christian believers, but of the pagan Roman Empire. Paul was admonishing not the overthrow of the pagan authorities by Christians but their submission to these authorities. Paul's attitude and that of the Christians during 250 years of Roman persecution stand in stark contrast with Mohammed and the Muslims of the 6th and 7th Centuries AD, who spread their faith by fire and sword.