This is an old post, but I thought I would comment. I am a home health nurse of 1.5 years with asthma and a severe cat allergy. All of my employers have been aware of my allergy before I was hired. I have specified that I would prefer to avoid the cats, but in a pinch, I should be able to wear a mask. We all know that the state of the home environment is highly individualized; while this might be acceptable for a home that is pretty clean, if there is a hoarding situation or just generally unkempt, a mask may not be enough to avoid a trigger. In the few times I have been in a situation where a mask just wouldn't cut it, my employer would make exceptions and I would trade patients with someone.
In my experience, almost every nurse has had a patient that they would prefer to not see, for one reason or another. Accommodations need to be made on a daily basis for reasons like this.
I have found that home health is in such high demand, that there will plenty of patients for me to see that do not have cats.
If you really want to do home health, don't get discouraged. Just be honest with the employer. If it is something they really don't want to deal with or can't accommodate you with, they won't hire you.
I'm really glad that I didn't let my allergies keep me away from home health.
For your info, I take Breo, Flonase, Singulair, Ventilin, and I carry an EpiPen. I was taking allergy injections for years, but I would never be able to tolerate the full-dose without having an anaphalactic reaction.