With all due respect, Dianne, I really don't think you can make a blanket statement like that. I am allergic to horses, dogs, and cats. I avoid horses like the plague, because having had little exposure to them, they cause me severe respiratory distress when I am near them. But I have had dogs all my life and didn't even know I was allergic until I had a horse episode when I was 11 and got generally tested. As long as I am around dogs on a regular basis, I am fine. When I would come home from college, I would have to avoid petting the family dog for the first day until I could adjust, and then I'd be fine.
I got a cat as a conscious choice to keep my dog company when I first started living alone and I had some reaction to her, but it was not bad. I woke up a couple of times at night to launch her off of my bed where she was sleeping near my face, and soon learned to simply lock her out of my room at night. As much as I would have loved her in my bed, it just wasn't to be. I also had issues once when I got a bad case of bronchitus. I had to make the dogs sleep downstairs until I recovered, but then I was fine again (I also had a doctor at this point tell me to get rid of my animals, but I think he never had a pet. There's no way I was turning out my 8-year old cocker that I'd had since he was 10 weeks old).
When I met my husband, he told me he was allergic to dogs and cats and I said that was too bad, because I had two dogs and a cat and they weren't negotiable. He decided to try to deal with his allergies and has been fine. We had a cocker and a sheltie. We currently have two Belgian Tervuren