I have some sympathy with the people suffering allergic responses - pet allergies are very common (much more so than peanuts or fragrances!) and can lead to life threatening asthma attacks. It's very difficult to avoid cats and dogs in daily life partly as a minority of pet owners are inconsiderate - my parents apartment block does not allow pets yet someone let their cat wander the corridors! The obvious solution is to make designate some flights as pet friendly and others not, if you wish to take a pet or specifically avoid pets you might be put out a little but the benefits for each party should outweigh the inconvenience.