If someone else chose to just give in to their allergies instead of dealing with them, i would think it was they who were turning my cat/dog/pony/parrot/etc. into a deal-breaker, not me.
I don't quite think that is fair. I stated earlier about how I am highly allergic to dogs, but my ex had one. I was able to be around his dog because of how he cared for his dog with the monthly baths and vacuumed regularly. Each dog is different. Each persons reaction to an animal to which they are allergic is different.
I've been on medication for my allergies for 20 years now, so for anyone to state that I'm giving in to my allergies is a bunch of hooey. I take pills, nasal sprays, inhalers and I've had allergy shots. I'm still allergic, and in some cases, it can cause me great difficulty. If I remove myself from a situation or a relationship
due to my allergies, it isn't giving in to those allergies. It's having respect for my body, and knowing what my body can and cannot handle.
I can only spend around 30 minutes in my Gramma's house because of her dog, before I start having problems breathing. A few weeks ago, I was in absolute misery because I was on a cross-country flight with a dog (which I hadn't known about until I was getting off the plane). I had thought I had come down with a cold from the traveling I'd done over the last week (two cross country flights in less than 4 days), but after hearing a few barks as I was walking towards the exit, I knew otherwise. I was sneezing so much (and so hard) that my nose was swollen for three days and faintly bruised, even after I'd stopped sneezing. My glasses couldn't sit properly on my face, it was so bad. At least now I know to ask the airline about any animals that may be on the flight, so I can talk to my doctor about other medications I can take to reduce the severity of my reaction.
I take all of my medications as prescribed. But if I were to have a reaction that severe to an animal that belonged to my SO, when on my meds, I'd have to make a choice... The person I am involved with (and their pet), or my health. My health would win. If my SO wants to make a choice of their own about keeping the animal, that is their choice to make. But I know that I won't ask them to make that choice.