The theory of “Fourteenth Amendment Incorporation” is generally agreed in by most constitutional law scholars, though you do find a few not on the lunatic fringe who object to it.
Bottom line is this: Section 1 of the Fourteenth defines all citizens of any state as citizens of the United States, and continues to guarantee them the rights and privileges of such citizenship, and prohibits states from removing them without due process of law.
The question then arises, what are the rights and privileges of being a “citizen of the United States”? And the answer that the SCOTUS identified, back in Gitlow v. New York in 1925, is that those rights protected as against Federal encroachment are, in general, protected against State encroachment by the due process clause. Justice Edward Terry Sanford wrote:
In general, the court has been inclined to identify such rights individually on a case-by-case basis, and in particular the rights of the accused as regards trials are not incorporated verbatim but with a view that state procedures may vary from those prescribed for federal courts but must result in justice and the due process of law or else will violate the protections of the Fifth and Sixth Amendments.
In this case, there is a general consensus that the erection of any artifact having a religious basis constitutes an “establishment of religion” in violation of the First Amendment, and a coercion against the “free exercise of religion” therein protected. The most common holding is that there is a “wall of separation between Church and State” which the state may not legally cross. Justice Sandra Day O’Connor is the current leading exponent of a second theory, that of religious neutrality, which says simply that the government is obliged to be neutral on issues where the religious beliefs of its citizenry differ. While they tend to arrive at similar results, the two theories do have some practical differences. For example, in time of a state of emergency due to natural disaster, the Constitutional authorization to protect the general welfare enables the government to provide assistance to those victimized by the natural disaster, as a purely secular act. Most religious groups also believe it to be a meritorious action in accord with their principles to aid such victims. SOCAS would say that government may not utilize the services of religious groups in channeling aid where it is needed; neutrality would say that this is perfectly acceptable, so long as it does not constitute a showing of government preference towards the beliefs of one group.
Now Judge Moore holds that to require him to remove the Ten Commandments from his courtroom would be forcing him to deny his God. (I report, I do not attempt to understand his logic.) The view taken by most liberals is that his displaying them is using state funds and the authority of the courts to give official credence to them, and in particular to the view of parts of evangelical Christianity that they constitute a special and focal element of what all men are obliged to obey. Many conservative Christians either cannot or will not grasp the perspective that this is indeed a mandate of Judge Moore’s religious beliefs on those who enter his court.
[Added close quote tag. – MEB]