You can catch a glimpse of this in Harry dealing with McGonagall if you remember that adults are significantly prejudiced against children, before his extraordinary intelligence overpowers and dissolves the situation.

Assuming their goal is to remove the prejudice, my guess is they would work within the confines of the prejudice where possible, towards changing the environment into a place where the prejudice is untenable. Something like agitating for a law that requires subservient tasks to be performed by the prejudiced group, then pulling a Fight-Club-esque "we drive your ambulances, we guard you while you sleep." In a smaller environment such as a woman in an unenlightened workplace, become the indispensable secretary to everyone and then punish the prejudice when it appears (changing the environment so that the prejudice is now directed at an authority figure).

It would be an unfolding plan rather than an impassioned speech and I expect would involve a lot of simple judo-ing of peoples' surface treatments of the issue.