Maybe you're right, but if you were in that kind of wave - I guess you mean the American civil rights movement of the 1960s, not the widely mocked PC movement of the 80s? - you were exceptionally lucky from a world-historical point of view. Currently, the same words might also be uttered by one of the hostage takers in the Iranian revolution, any member of the Taliban, or one of the older prison guards at a concentration camp in Xinjiang. (Really. Imagine each of those people saying that sentence). Point being, those words usually sound absurd to anyone who doesn't share your political and cultural frame of reference.
I'm also not really interested in picking out specific movements, because I suspect that, on a forum like HN, that would do more to muddy the waters by encouraging further rhetorical cherry-picking. This is a forum that tends to incentivize scoring cheap points over sober, pensive discussion whenever social issues come up.
That said, I saw it go the other way for some of the issues that one of my older siblings was excited about back in the day.
It's just possible that, "This idea seems to be most popular among young people," doesn't actually function as a stunning rhetorical coup de grace for any side of any cultural debate.