For example, “If you meet a stranger in a coffee shop, do you notice their (or his or her) smile?” becomes “If you meet strangers in a coffee shop, do you notice their smiles?” This particular example doesn’t provide the most elegant demonstration of the technique, but try it with “When I meet a potential client for coffee, he or she is usually late.”

ahhh!!!! are you allowed to use the passive voice?
Your predicated argument assumes that the writer’s gender always “suggests an appropriate gender” for the pronouns.

don’t ever be passive when smacking aaron.

sorry, lisa, i just got bickering-envy.
fabulous, site by the way.

Thanks a lot for your site.

Your original post said that if you were the ruler of the grammatical world, “the correct usage would be to simply match the gender of the writer.” Even if we qualify that to say “unless the content suggests an appropriate gender,” I would disagree. I have never seen anything written that way (i.e., because the writer is a “she,” female pronouns are used), and I see no reason why the gender of the writer should cause the content to be skewed “feminine” or “masculine.” A man isn’t necessarily writing about men, nor a woman about women.

Methinks we’ll have to agree to disagree on this one. I think we’ve just proved the point that it’s a tough issue.

You silly goose.

As a simple minded person, I notice their smile, unless I want to bring gender into the equation, then I would use her or his. I emphasize simple minded.