Your analysis looks correct to me, but if you think in terms of "causing friction", you're using an assumption of personal responsibility that makes you exploitable in a game-theoretic world.
If person A would benefit from stereotyping person B, and person B doesn't mind being stereotyped, then person C can screw up the chance of that positive-sum interaction happening by precommitting to be very offended if A stereotypes C (or even B). Game-theoretically this is like threatening to burn other people's money if an undesirable event occurs. To determine who is "wrong" and who should change their behavior in this situation, you probably need to look for arguments outside the game. Maybe A is wrong by stereotyping; maybe B is wrong by condoning A's behavior and betraying the group; maybe C is wrong by screwing up others' positive-sum interactions. But if you just assume that any offense is always the "fault" of the one who offends, you're ignoring the reality of people who take offense to further their own goals, consciously or subconsciously.
One possible solution is to use aggregate utility. Would the world contain more utility if stereotyping didn't exist - compared to a world where stereotyping is widespread and no one takes offense? If yes, then you can make a case that stereotyping is analogous to defection in the PD. If no, then you can make a case that taking offense at stereotyping is like defection in the PD - it benefits your group, but hurts the world overall.
Speaking of precommitment to be offended. Would a perfectly rational B be offended at all by an incorrect guess? Granted, humans aren't perfectly rational, nor do they exist in a vacuum.
I'm rarely genuinely offended by stereotyping - I prefer to just politely point out the mistake. Sometimes, though, I prefer to act as if I was offended if it's socially acceptable to be offended in the situation and I believe it's in my interest to further my goals.
During discussion in my previous post, when we touched the subject of human statistical majorities, I had a side-thought. If taking the Less Wrong audience as an example, the statistics say that any given participant is strongly likely to be white, male, atheist, and well, just going by general human statistics, probably heterosexual.
But in my actual interaction, I've taken as a rule not to make any assumptions about the other person. Does it mean, I thought, that I reset my prior probabilities, and consciously choose to discard information? Not relying on implicit assumptions seems the socially right thing to do, I thought; but is it rational?
When I discussed it on IRC, this quote by sh struck me as insightful:
I came up with the following payoff matrix:
In this case, the second option is strictly preferable. In other words, I don't discard the information, but the repercussions to our social interaction in case of an incorrect guess outweigh the benefit from guessing correctly. And it also matters whether either Alice or Bob is an Asker or a Guesser.
One consequence I can think of is that with a sufficiently low p, or if Bob wouldn't be particularly offended by Alice's incorrect guess, taking the guess would be preferable. Now I wonder if we do that a lot in daily life with issues we don't consider controversial ("hmm, are you from my country/state too?"), and if all the "you're overreacting/too sensitive" complaints come from Alice incorrectly assessing a too low-by-absolute-value negative payoff in (0, 1).