Depends on B's preferences. If B is selfish or cares about their group disproportionately, then yeah, it may be perfectly rational to take offense.
I'm not an aggregate utilitarian - I believe it's okay to be selfish at the expense of everyone else (within limits, e.g. I wouldn't nuke New York to get an ice cream). But from the viewpoint of total utility, you may or may not be hurting the world overall by adding "friction". I'm kind of on the fence about this - please don't take my grandparent comment as claiming that taking offense is always negative-sum. I was just pointing out the possibility, but to get the right answer you have to imagine the two worlds and calculate.
Hmmm.
I wonder, then, if it's logically coherent to talk about a world where nobody gets offended by stereotyping without changing something fundamental about humans. Are we sure we'll be talking about a human world in that case?
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).