On a flight last week, a woman took her dog out of the carrier and put it on her lap. I asked a flight attendant about this because I though it wasn't allowed. He told me they are not allowed to ask people to put their pets away because they may be emotional support animals. He said a memo came out about this a few months ago that FAs are not allowed to question people about their pets.
Whether this extends to rabbits or not, who knows. I was once on a flight from ATL to CDG with several birds in the row ahead of me.
I agree with the post that said many animal lovers don't understand that there are some of us out there who just don't like them all that much or want to smell them.