My wife and I both have had minor pet allergies. When we would go to houses that had pets (especially poorly cleaned ones) we would both have mild reactions ranging from coughing and sneezing to itching eyes. My wife also would develop rashes that would sometimes develop on her hands in response to dog saliva. Given the number of family members and friends with dogs we faced this a lot.
When we were talking about getting a dog I was concerned that this might become an issue. My wife assured me that she felt the sacrifice would be worth the rewards, and that she also thought that she could keep the house clean enough to reduce exposure. I had my doubts but instead of arguing I made sure I knew where I could get a burlap drowning sack just in case the puppy needed to go. After getting the dog I noticed some minor irritation but my wife's allergies were a little more pronounced. Not nearly as much as when she'd go to our friends' house with their three large dogs, but bad enough to make her uncomfortable. When I raised finding a new home for the dog she soundly rejected the idea saying that she had made a commitment and we were going to keep her.
About a month later my wife noticed her reactions were less pronounced. Whereas before licks to her neck and face would cause itching, now she has no problem with it. Her nose is still a little congested, but her hands - always sensitive to dog saliva and dander - weren't breaking out. Better still, when we visited our friends with the big dogs over New Year's eve she had no problems at all. Other than a little more coughing than usual, neither did I.
Turns out immunotherapy works if you can see it through, and better still it can be applied with daily doses in puppy form instead of through injection.
I guess exposure to unpleasant things really can serve to strengthen you and safe spaces only result in nurturing weaknesses.