What was the rationale of the dissent in the Slaughterhouse cases with respect to Article IV and the protections afforded to U.S. citizens by the XIV Amendment?
I assume that you are asking about Justice Stephen Field’s dissent in this case. Field argued that the Fourteenth Amendment protected people from actions by the states, not just the federal government. He also argued for a broad interpretation of the due process clause of that amendment.
The majority opinion in this case held that the Fourteenth Amendment applied only to the rights given to people by the Constitution. It also held that the amendment was not really meant to protect anything except the rights of the freed slaves. Therefore, the Louisiana law at issue in this case (which applied to slaughterhouses, not to racial categories) was constitutional. It was a law that did not infringe on any liberty given to the people by the Constitution. The Constitution does not give anyone the right to put a slaughterhouse wherever they like. It was a law that did not discriminate against people on the basis of race.
Field, by contrast, held that the Constitution and the Fourteenth Amendment were much more important than this. He held that they protect all fundamental rights that people have. Among those is the right to liberty. He interpreted “liberty” to include economic liberties as well. What Field was saying is that a state cannot enact laws that take away from people’s economic liberties. His dissent would become the basis of the “substantive due process” theory that would be in force until the time of the New Deal.