From a quick Google search, there doesn't appear to be medical evidence of any life-threatening allergies to pets like dogs.

That also apparently hasn't stopped people from claiming they have one, however.

I also did some googling and reached broadly the same conclusion as you. However I don’t know that I’d use the word "any”. It sounds like life-threatening animal allergies are, at the very least, much rarer than life-threatening food / medicine allergies. Though I wasn’t super satisfied with any of the sources I found, so I’d love to see some data about it.

Cat dander can and will affect certain people pretty badly.

I would imagine they ask if anyone is willing to trade seats or move them to an unoccupied seat.