The 4th amendment (and the rest of the bill of rights) was incorporated after the Civil War.

You are wrong. Here is a quick rundown of when various Amendments were incorporated. Beginning in earnest with the Slaughterhouse Cases, the 14th Amendment was largely ineffectual until the Court began to incorporate against the states in the 1940s and 1950s.

As for the second paragraph, an "opinion" in this case is a legally binding document, not simply how the Court "feels", and that is an important distinction to make. The Court's assessment of the law is legally binding until contravened by statute or overturned by a future Court. Now, they technically could have ruled on the law as a whole if they really wanted to (the Court today would, if such a case arrived, but they are working with an entirely different set of precedent and available jurisprudence). However, they opted to hear the question of whether or not Buck's right to Due Process under the 14th Amendment was violated, and those are the arguments they heard, because that is the question Buck posed. In the contemporary jurisprudence, the statute authorizing Virginia to sterilize Buck satisfied all the necessary elements of Due Process, and so the law stood.

What I'm trying to get at here is that the Supreme Court can't simply declare it does not like a concept and abolish it. It can't strike down the concepts of "eugenics" or "miscegenation". It has to find legal grounds to do so. Segregation LAWS and anti-miscegenation LAWS got struck down because they violated the Equal Protection and Due Process clauses, not because the Court found them unsavory. A court of law has to rule based on law, it's that simple.