In 1877, Davidson v. New Orleans, the Supreme Court noted:
It is easy to see that when the great barons of England wrung from King John, at the point of the sword, the concession that neither their lives nor their property [and their liberty] should be disposed of by the crown, except as provided by the law of the land, they meant by 'law of the land' the ancient and customary laws of the English people, or laws enacted by the Parliament of which those barons were a controlling element. It was not in their minds, therefore, to protect themselves against the enactment of laws by the Parliament of England.
In other words, "due process of law" didn't mean the courts could overrule acts of the legislature, the Parliament deemed supreme. In fact, there was some hint (see, e.g., Coke) that there was a "higher law" even there, a hint American colonists seized upon, but by the 1760s things were generally more conservative in England. But, to continue:
But when, in the year of grace 1866, there is placed in the Constitution of the United States a declaration that 'no State shall deprive any person of life, liberty, or property without due process of law,' can a State make any thing due process of law which, by its own legislation, it chooses to declare such? To affirm this is to hold that the prohibition to the States is of no avail, or has no application where the invasion of private rights is effected under the forms of State legislation.
Our Constitution, however, sets forth a limited government, including guarding against laws that invade areas where the state has no business going ... for they are not "public" at all, but matters of "private" concern ... "private rights" are referenced in Federalist No. 10 and 78, the latter underlining the role of the courts in securing them:
But it is not with a view to infractions of the Constitution only, that the independence of the judges may be an essential safeguard against the effects of occasional ill humors in the society. These sometimes extend no farther than to the injury of the private rights of particular classes of citizens, by unjust and partial laws. Here also the firmness of the judicial magistracy is of vast importance in mitigating the severity and confining the operation of such laws.
The value of "or has no application where the invasion of private rights is effected under the forms of State legislation" is ever more clear in this more intrusive (and conservative in some cases) age. There are limits to the police power (fans of the 10th Amendment need to read the whole thing) ... consider the power over "public morals." There are "private" morals too. This word is sometimes misunderstood (or purposefully mishandled) -- it does not mean totally secret, nor only affecting the person themselves (what does?), nor that the government cannot regulate. They can, with care, and it does particularly affect matters of private concern, often particularly affecting the person in particular.
The ruling cited has a famous quote about how the due process clause was used so often (often by corporations), much more than the words reasonably could bear. "There is here abundant evidence that there exists some strange misconception of the scope of this provision as found in the fourteenth amendment." So, if there was a means to cabin it, to interpret it in a crystal clear matter, it would be ideal. But, life, alas, is a bit more complicated:
But, apart from the imminent risk of a failure to give any definition which would be at once perspicuous, comprehensive, and satisfactory, there is wisdom, we think, in the ascertaining of the intent and application of such an important phrase in the Federal Constitution, by the gradual process of judicial inclusion and exclusion, as the cases presented for decision shall require, with the reasoning on which such decisions may be founded. This court is, after an experience of nearly a century, still engaged in defining the obligation of contracts, the regulation of commerce, and other powers conferred on the Federal government, or limitations imposed upon the States.
This includes a case in 2006, Justice O'Connor's swan song, where an UNANIMOUS ruling (AYOTTE V. PLANNED PARENTHOOD) held:
our precedents hold, that a State may not restrict access to abortions that are "necessary, in appropriate medical judgment, for preservation of the life or health of the mother."
Things are a bit more hazy now ... but so it goes. Another century plus has passed since 1877, and the courts continue their labors. The Supremes have law clerks now and a smaller caseload, but that's a different story. But, things also stay the same. In Federalist No. 10, Madison spoke of the "alarm for private rights" being threatened by dangerous factions (interest groups etc.).
Sound familiar?