From a traditional Liberal political position (perversely now seen as 'libertarian' or conservative) these two things serve different purposes, and do not conflict. If you take "natural law" literally in English, it includes things like gravity. Gravity predicts, it does not prescribe. Other forms of natural law are parallel to that. What is likely should not be surprising to the law, and it should accommodate what is inevitable, or even too common to resist with any consistency. This is the old saw "You can't legislate morality."
From a Lockean perspective, expressed law exists to make space for individuals to express their own natural order. The liberal tradition intends to create freedom, to keep different subcultures out of one another's way when that is possible, and in all other respects to minimize action. This is a reason given by many traditional threads in U.S. culture for why the American founders (strongly influenced by the dominant English philosophy of their time) use so much negative language in the first ten Amendments to our constitution (language that is not as clear as the amendments move forward).
So I feel your question has skewed the terms in which it is expressed.
The problem, from an old-fashioned 'social contract' position may be that people incorporate whatever they get too used to into their morality and make of it a sort of secular religion. So if you are not legislating morality, but the law is a constant presence in society, what you legislate is taken to represent a prescriptive morality.
Given the basis of liberal democracy (in the U.S., the part of the First Amendment that forbids 'establishing religion' and mixing Church and State) Governments have no business blocking other sources of order. But the emphasis on the 'rights' and 'freedoms' point of view develops into a moral principal of continual defiance and struggle against natural structure. Making space becomes a moral imperative, even when there remains nothing left to fill it.
It is exceptionally tempting to legislate morality when the moral sentiments themselves originate in the way your laws are expressed and represent a striving for some kind of consistency and completeness in what is purposely meant to be a minimal and therefore partial solution. It is something we almost automatically do. This is the corresponding Hobbsean perspective balancing Locke. Political systems hate being limited, much less minimized. Forces have to intervene and limit the powers of government, and return them to the restraints they were designed to live within.
So what you are pointing at is a disease of modern governments, and not part of their nature or intent. The way to resist this is to insist on the original notion of the State on which modern countries are constructed. You are to be free to seek your natural order. That is the point. And if they are interfering with that, they are well beyond their mandate, and the State is corrupt.
This is one way of looking at the current U.S. Presidency. The election of an unqualified player who obviously does not understand the system he is being expected to take part in and keep running was via 'protest vote'. People are insisting that the system is overgrown, the world is too complicated, and they want to hear simple solutions or just watch things break, so they can be swept away. So they elect someone who cannot understand or navigate the legal system, and has shown little intention of trying to do so. He represent their own inability to understand what is going on, and lack of concern for maintaining it. The more openly he fails, the more we as a society approve of him.
Anarchists are a real example in the U.S. The 'sovereign' retreat from interaction with the government, and protect themselves with the laws that honor religion forming among others the Rainbow Family. They defend themselves by becoming public victims whenever the authorities cross their path. Extreme conservatives do the same thing, in the form of the Amish and collectivist Mennonites. Freedom can be used to create structure in isolation. Less extreme versions of the same tactics can maintain a traditionally structured community, for instance the Hasidic to some degree enforce their own parallel law even in large cities.
