I can answer this...

A few years ago I noticed a woman with a cat sitting in the gate area. Being very allergic to cats, I quietly went to the GA and asked if she could check if we were seated near each other. Of course, the cat owner was seated directly behind me, which meant the cat was under my seat. I've been hospitalized twice for allergic reactions to cats, so I don't play around with this.

The GA offered to move my seat, but I was in the second row and needed to make a quick connection. Plus, I was PM. The woman with the cat was called to the counter and told she had been moved to the last row, and would be both boarded first and remain on the plane until everyone else got off. She was also told she could not take the cat out of the holder. At first, she started to complain, but the situation was explained to her and she was very cooperative. The GA also explained the situation to the FAs, who assured me they would keep an eye out.

Hopefully all pet owners are this cooperative and don't think that it's acceptable to take the animal out of the holder after take-off.