When we try to explain Christian morality today, too often the arguments are framed in the language of "divine command theology" where we simply take it for granted that just because the Bible tells us that God ordained something and it was recorded means it is so. Obviously this is not convincing to people who haven't made some a priori acceptance that the Bible is at least mostly true. For most people, this approach is little more than a naked assertion. So what if the Bible says that homosexuality is an abomination if you don't already believe that the Bible is the Word of God?
What we need is a way to convince people that these things are more than just naked asertions to be taken on blind faith, but rather are rational, reasonable and can be seen at work in the order of the world around us. For generations, Christians relied on natural law theology to convince non-Christians that Christianity was not only rational, but fundamentally reflective of the world around them. Borrowing from the Acton Institute and Cicero, natural law is...
a true law, a right reason, conformable to nature, universal, unchangeable, eternal, whose commands urge us to duty, and whose prohibitions restrain us from evil. . . . It is not one thing at Rome and another at Athens; one thing today and another tomorrow; but in all times and nations this universal law must for ever reign, eternal and imperishable. It is the sovereign master and emperor of all beings. God himself is its author - its promulgator - its enforcer. He who obeys it not, flies from himself, and does violence to the very nature of man.
The Acton Blog has a great treatment on how and why modern Protestants began to have a strong aversion to natural law theology in any form. Here they are.
The existence of a natural law was not debated in the Bible, but was actually taken for granted. The moral law of the Old Testament combined with human reason and intuition instructed by the same is what we know as natural law. From the moral law, we know what is good and evil, from reason we can apply those laws to complex scenarios such as ascertaining when a government has rendered itself illegitimate. The Apostle Paul referred to natural law in a limited scope in both Romans 1 and 2 in reference to sinners having known from the beginning what was good and what was evil, and the fact that gentiles often behaved in ways very similar to the pure, revealed form of the moral law given by Moses:
18The wrath of God is being revealed from heaven against all the godlessness and wickedness of men who suppress the truth by their wickedness, 19since what may be known about God is plain to them, because God has made it plain to them. 20For since the creation of the world God's invisible qualities-his eternal power and divine nature-have been clearly seen, being understood from what has been made, so that men are without excuse.
12All who sin apart from the law will also perish apart from the law, and all who sin under the law will be judged by the law. 13For it is not those who hear the law who are righteous in God's sight, but it is those who obey the law who will be declared righteous. 14(Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law, 15since they show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts now accusing, now even defending them.) 16This will take place on the day when God will judge men's secrets through Jesus Christ, as my gospel declares.
To expand on Paul's points, natural law theology offers Christians a common starting point in dealing with many other religions, as most major religions are based on a large portion of the moral requirements referred to by both Paul and Cicero. This similarity allows Christians to appeal to them on the grounds of an ancient shared heritage and to guide them to the realization that Christianity is, in fact, the final form of that ancient shared heritage which traces its origins to the foundation of the world by God. The moral law of the gentiles that Paul referred to is a form of the natural, universal law.
The explanatory power of natural law is sadly missing in many Protestant churches which frequently make statements like "anything the government does to you is acceptable, until it violates God's law." However, such statements are not entirely correct. There is a universal law which applied as much to the Roman Emperors who ordered persecutions as it did to those persecuted by them. God may grant authority over people and property, but a grant of authority should never be confused with legitimacy from that point onward as legitimacy can only be conferred by right action. A head of state may rise to power with the permission of God, but their actions can just as easily render them an illegitimate ruler, even a criminal, according to what we know from reason and revelation about good and evil. A ruler who wantonly slaughters the innocent is no less a criminal than common man who does the same. A ruler who visits unprovoked violence on peaceful people is no different from a common man who does the same to his neighbor.
I think too often Protestants fail to realize why it was that the early church chose martyrdom over insurrection. Martyrdom, especially at the hands of a government that is doing blatant evil is a very powerful form of revolt because it exposes a raw, unavoidable difference between the aggressor and their victim. It leaves the former with no defense, as all witnesses can see that the victim didn't even fight back, thus all of the action is directed toward the victim, and the aggressor's actions are exposed for what they are to all people of decent character. Those same people begin to question what could the victim have possibly done to deserve that violence, and in the process often become naturally curious about who the victim was and what motivated them.
Aside from all of this, natural law theology can also serve to remind the church of the line between religion and spiritual life. Natural law theology confronts us at different times, and reminds us that there is more to the dictates that we see in the Bible. We can see them play out in the very fabric of the world itself and human nature. The universality of natural law can also be a bulwark against modern secular non-judgmentalism and multiculturalism which teaches us to never judge the constructs of another belief system, no matter how blatantly absurd and irrational they may be.
I suspect that most modern American protestants would not be at ease with a return to natural law theology because of the way that it would shape and mold their beliefs. American protestants have grown accustomed to the "right of schism" the moment that their cherished beliefs clash with their church or another religious authority. Natural law theology is inherently incompatible with that tendency because of its basis in the authority of revelation and insistence that reason is integral to faith.