Is it normal that I don't want to date someone that's allergic to dogs?
It's not that weird of a request, if I may say. Is that a deal-breaker for you?
I would feel bad if my dogs aggravated their allergies.
Just let your future dating partners know you have dogs and don't intend to make exceptions for their allergies. Tell them your dogs come first.
My dogs are part of our family, so yeah, you are right and that I need to just be patient and find the perfect girl.
Your dogs were part of your family first, so they really would supersede the person that you end up dating. Plus, it's not inappropriate to ask your date if they have dog allergies because it shows that you care about the person as well, and if the person doesn't care, even with allergies, it's probably a really good sign that they love you.