What was Rehnquist’s reasoning? He wrote:
To the argument made by Thurgood Marshall [in Brown v. Board of Education] that a majority may not deprive a minority of its constitutional right, the answer must be made that while this is sound in theory, in the long run it is the majority who will determine what the constitutional rights of the minority are.
Thus, the rights of minorities are whatever a democratic majority says they are — and the “transient majority of nine men” (the Supreme Court) is not empowered to overrule a democratic majority in order to defend minority rights. According to Jack M. Balkin, Rehnquist was correct that minority rights are whatever the majority decides — but Rehnquist still missed a key point.
What Rehnquist missed is that sometimes the majority enshrines rights for minorities that even a democratic majority cannot easily take way or define out of existence:
...because it serves their own interests, because it helps shore up the country’s legitimacy, or simply because they have come to believe, as a result of a long process of social movement contestation, that a minority is not being treated fairly, and protecting their rights is just the right thing to do. ...The meaning of highly abstract terms like liberty and equality is continually being contested in everyday politics, and struggles over the meaning of liberty and equality eventually have long term impacts on the beliefs of Americans, and on the beliefs of those who form part of the dominant political coalition in the United States.
At the time, the nation’s views on race and civil rights were changing. Not everyone had come around to the idea that there should be equal rights for all and even today there remain a few who are convinced that different races deserve different treatment. Nevertheless, there was enough of a consensus that justified the imposition of national values on the Southern states that were continuing to hold out. The same, ironically, is very much true today when it comes to sodomy and gay rights.