I've flown with cats a few times, and most recently on AS on a pretty empty flight so I picked a seat that would be away from other people.

AS (and most other airlines) policies allow some number of pets per cabin - for AS it's 5 in Y and I think 1 in F. Should they rebook all 6? I'd gladly move seats to keep the cat away from someone with an allergy, and it's fairly common for people to not even notice a pet until you're getting off the plane. I've had that happen when I was traveling with a pet and seen it with others. Aircraft turn over the inside air pretty quickly and pets aren't alllowed out of their travel carriers, so the amount of dander more than 1 seat away should be extremely low. One thing airlines could do for the $100 that they charge to bring a cabin pet is keep packets of anti-dander wipes at check-in and hand them out to passengers when they check in with their pets. It's not quite as good as an anti-dander shampoo, but it should reduce the allergic effects reasonably well for the duration of most domestic flights.