1795 Flying Pets

I heard on the radio that one of airlines has opened up their pet policy. They’re going to allow any service animal, with an appropriate doctor's prescription, even if that animal is a monkey or a lizard.
Up to now, most airlines have only offered dog and cat onboard privileges, although some allow birds. Which seems a little odd. A bird flying in a plane is like a fish riding a submarine.
Be that as it may, I wonder where the rights of one trump the rights of another. If by service animal, they mean one who assists the deaf or blind that's one thing, but how about the broader category of the psychological service animal? Those brought along to comfort their owners.
Because I know plenty of people who have physical allergic reactions to dogs, cats, and pet dander generally. What about their rights? Do they have to add additional allergy assistance just because someone else can't fly without Fifi or Fido?
Where do you draw the line?
Or how about the poor person who has a morbid and debilitating phobia for four-legged fiends? Can they bring their counselor on board for a reduced fee?
I remember a woman who brought a dog into an establishment were I worked a long time back. The dog started to growl at me. In my workplace.
And it stunk to high heaven. I had to open the doors to air the place out afterwards. The lady was exercising her right to bring her stinky dog with her. But what about my right to work in a dogsmell-free environment?
She wouldn't have been able to walk in with a cigarette burning. Why should I have to inhale her stinky dog?
As you can tell, it got my dander flying...
America, ya gotta love it.