I'm going to push back on one assumption here: the Supreme Court doesn't "force" things. The Supreme Court declaims a principle of law that compels the outcome of a certain case. That principle will, then, in all likelihood, have broader applications. But especially in hot-button issues, the principle does not translate immediately into action.

The most drastic example is Brown v. Board of Education, 347 U.S. 483 (1954), where the Supreme Court held that separate-but-equal educational facilities contravene the Fourteenth Amendment's guarantee of equal protection. The decision itself required the defendant school district to integrate. The principle announced in the decision meant that all other schools, by extension, would also have to integrate. But they did not. Instead, the South adopted a policy of "massive resistance" to avoid integration. This effort successfully stalled integration. Indeed, the next year, the Supreme Court was forced to decide another case -- Brown v. Board of Education "II", 349 U.S. 294 (1955) -- directing the federal district courts to take jurisdiction of desegregation cases, and enforce the Court's directive "with all deliberate speed."

Even that wasn't enough. In 1957, President Eisenhower was forced to deploy the 101st Airborne to protect nine black children attempting to attend an integrated school in Little Rock, Arkansas. Litigation over the proper remedies in Brown -- such as, busing -- would consume the Court's docket, the Senate calendar, and the attention of the White House for the next several decades. Edit to clarify: if you are interested in learning more, any constitutional law textbook will contain a detailed history of this development. I'm happy to recommend a specific text if you are curious.

I mention this because despite the Supreme Court's decision in the interracial marriage case -- Loving v. Virginia, 388 U.S. 1 (1967) -- some states did not abolish their mixed-race marriage laws until the turn of the century. That doesn't mean that mixed-race couples couldn't get married in Alabama until 2000. But it illustrates my point about the difference between judicial decision and change on the ground. Because of how controversial race issues were in the 1950s and 1960s, despite the Supreme Court's decision, the world did not simply turn on a dime. If you were to look back, you might not, then, see mixed-race couples lining up in Alabama the day after Loving was decided.

The two people for whom the Court's decision in Loving made an immediate difference were the plaintiffs -- Mildred and Richard Loving. They had already married, in Washington, D.C. But the Court's decision meant that their decision to do so, and to live in Virginia as man and wife, was no longer illegal, and they could not be jailed for it.