@Lisa723
In the link you posted unfortunately Airbnb don't distinguish between live-in Hosts and absentee Hosts renting their properties. It's clearly vital to do so, because a live-in Host may not wish to have any animals in their home, pets or otherwise, principally for health reasons. From this perspective an animal is an animal whatever further label we wish to put on it, and is prone to certain diseases; similarly may affect persons with allergies.
Personally, I've never encountered the problem. I've only dealt with the 'pet' variety, Guest wishing to bring their pooch having either read or not read my 'no pets' house rule. In any case, I simply decline politely and inform them to look for listings that fit their requirements.
However, If I was to receive a 'service' animal inquiry, I don't believe it would be so difficult to deal with as I also don't subscribe to Instant Book.