I don't know any scientific theories, but this is my experience.
I grew up with dogs and horses and never suffered any sort of allergy to them.
Then I left home, went to uni and bought my own house, and stopped riding, and had no dog.
Now when I go and visit my Dad, who has a dog, I sneeze like mad.
DH on the other hand was always allergic to cats, and when one decided to move in with us, as they do, he sneezed and had very itchy skin. The cat refused to move out though, and within a few months these symptoms disappeared. Now DH, DS, the cat and I all live happily under the same roof with no problems.
DS does wheeze a bit and gets mild excema but it's not cat related - he wheezes when he has a cold and gets excema when we use bubble bath or soap to wash him, or don't moisturise him enough.
My (very unscientific) theory after all this, is that some people can build up a tolerance to allergens if exposed to them on a regular basis - it certainly seems the case with DH and me, and DS isn't allergic at all.