Feminists

To persuade someone, you first have to identify your existing common ground -- the fundamental values that you share. Then you proceed from there to see whether their specific positions are consistent or inconsistent with those values.

The problem that arises, of course, is that the fundamental values that we all share (not just us good guys) are in fundamental conflict from the outset: we all value freedom, and we all value security, for ourselves and for everyone. It becomes a question of which side each of us comes down on on any particular issue: freedom/security, me/the rest of you.

But it is still the only way to begin a persuasive argument. With your n-word/c-word example, start by identifying the facts relevant to the decision in the first case (historical disadvantage, etc.), the values to which the proscription on the one responds, how the proscription promotes or infringes one value or the other, how it subordinates the me to the rest of you or vice versa, and how your interlocutor conducted the balancing and tradeoff exercise to arrive at their preferred result.

Then apply it all mutatis mutandis to the other group. Your interlocutor needs to come up with relevant distinctions in order to reject the proposal that the two are like and must be treated as like. If "free speech" doesn't defeat a prohibition on one word, then it can't defeat a prohibition on the other word, unless there is some distinction between the situations that actually operates to make them unlike in a material way.

The huge barrier to doing this here, I'd say, is just the monumentally incivil discourse that is practised and rewarded here. One cannot ask a simple, straightforward question without being met by diversion; one cannot make a simple, straightforward statement without being met by misrepresentation. And always the character assassination at every turn.

Maybe somebody could model the process for the audience here.