Should social change be promoted through the court system or the political process?
This is, of course, a matter of opinion. My own view is that the judicial system can be a good way to get some change, but that real systematic change only comes through the political system.
The judicial system can be a good way to pursue change because it does not involve having to convince large numbers of people of the rightness of your argument. If you can convince a few judges that your interpretation of the Constitution is correct, you can achieve things that would have been very hard to achieve through the political process. The Brown v. Board of Education case is a perfect example of this.
However, change that comes through the courts is not as broad and as sweeping as change that occurs through the political process. The reason for this is that the courts can typically only rule on a limited area of law. By contrast, the elected branches of government can create any sort of law that they want. They can do much more for a movement than the courts can. As an example of this, the 1964 Civil Rights Act did much more to advance the cause of civil rights than the Brown decision did.