How exactly is Brown vs. Board judicial activism? It's been a long time since I read that case, and I'm not sure I ever did. But I am aware it prohibits having separate but equal/segregated schools.

The schools, of course, weren't equal. The constitution plainly states that laws treat people equally. It seems that's what the decision was all about. So how is that activism? Sure it changed the policy, but it changed the policy in accord with the constitution, and not for policy reasons.