No I think (just as I thought when teaching racial equality to children whose parents were racist) that you tell the child that within the school environment they should treat everyone with consideration, and respect, and accept their equality. That means not calling them "crazy" saying they need mental help or should be in an asylum or denigrating them in any other way.
Your views may be anything you wish, but if they are permitted to make another child uncomfortable then that is not acceptable and the school will have to take action.
I suspect that I would feel uncomfortable sitting next to someone who identified as a cat, depending on how that manifested. It would be distracting at best. Would that be taken into consideration?
Race, sex and other immutable characteristics should absolutely be respected, as should religion - which means amongst other things that there should be single-sex facilities.
Pupils of whatever sexuality should be treated the same, whether they are gay, straight or bi. Some aspects will be noticeable, and others not, but it shouldn't matter in a school context beyond it being unacceptable to treat people as different because of it.
Children who believe that they are the opposite sex should not be bullied for it (nobody should be bullied for any reason), but I don't think that gaslighting other children into having to say that they are seeing something that they are not - ie a boy is a girl or vice versa, and that applies to seeing a child and not a cat. I'm not saying that anyone should say that the child belongs in an asylum, but nor do I think that it is 'despicable' to say 'no, you are really not a cat'.
Race, sex and sexuality are different things, but they are constantly conflated on here, which is frustrating in the extreme. Is identifying as an animal now joining the conflation?