I am loath to criticize anyone holding his ground against the forces of singular they/their. However, I do concede that it’s possible to take things a little too far.
I follow the Associated Press Stylebook* in matters of animals and pronouns: “Do not apply a personal pronoun to any animal unless its sex has been established or the animal has a name. The dog was scared; it barked. Rover was scared; he barked.”
Given the fastidiousness with which the CitiBank sign is worded (“Please ask…”), I was surprised to see “a assistant.” And as long as we’re talking about correctness, why “pet” instead of the PETA-approved alternative, “animal companion”? Come to think, why not just “dog”? Perhaps some disabled persons now use chickens to cross the road.
* The AP would have some stern words about CitiBank’s erratic capitalization, too.