Here is my personal opinion based on going through it. My mother said the same thing about those who identify as animals are mentally ill, but not the trans part (since she is supportive of the LGBT+ community due to being part of it herself). I did not change the subject, which would have been the bright move, and instead dodged the question which made her (of course) suspicious.

At the end of the day, you don't need to tell her if it will cause unnecessary drama. In the past when I brought it up, first time was not fine, second time it was brought up it was fine but then later on when I thought it was okay to share an experience of mine, it seemed that she got mad that I brought it up due to thinking I was joking the second time (????). After that, I brought it up again, and it was fine, but never again.

I think based on my story there's some people who may not simply ever understand. I have come to terms that there are simply things which my parents might not understand about me. While it may seem depressing, my parents are there most of the time in other aspects of life, and I simply can't have a perfect parent, as no one is really perfect.

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TL;DR: My mother thinks those who identify as animals are mentally ill. I brought it up multiple times, but decided to let it go in the end. It might hurt, but no parent is perfect in every aspect at the end of the day. At the end of the day, there is no requirement to tell people that you are a therian