It absolutely does work. A little bit, at first, when you have broad consensus backing you - but it does work. People will begrudgingly change their behavior for relatively minor things, and the change in the use rate of racial epithets in public reflects that.

The problem is that A) this process is more useful for advancing within the ideological block than for advancing the ideology's goals, and B) there's a "Laffer Curve" of sorts for paying "moral taxes" in following behavioral norms. The internal dynamics of a movement is going to set the level by true-believer dynamics where outrageously high demands are acceded to, while the general public is going to respond to that level of demand of "well, if you think I'm a bad person for saying 'Latino" instead of 'Latinx', that's your problem".