Do transgender genders in animals exist?
Gender is a complex subject. This question though enters a whole new dimension of complex because we cannot effectively communicate with animals to ask whether they understand the concept of female and male and which they identify with. Before delving into it further, we know animals have no or close to no concept of self, depending on the species. Some sea mammals can and do recognise themselves in mirrors so we think there might be some concept of self and therefore maybe even gender. Additionally a sense of slef is not excusively measured through interactions with a mirror. Proprioception is another important measure of self awareness. Many transgender humans report a mental body image that is different from the reality, where the missing parts are neurologcally sensed. This is more known as phantom penis/breats.
That said, having a higher order concept of self may not be essential in taking up gender roles or performing gender-typical behaviours because many such things are governed by the different sizes of brain structures, which reflects the amount of connections made in these structures.Studies in the physiology of the brain have found dimorphism in certain brain structures between males and females. Moreover M2 females and F2 males are more likely to exhibit behaviours of the opposite sex which become more pronounced if the animal is neutered, and to have brain structures similar to the opposite sex's.
I think it is perfectly possible to say yes there are without antropomorphising. It is unlikely that animals consciously want to be the opposite sex and want to change their image to align with that. They probably just live the life they know and make the best of it. For example my dog, although I have no way to confirm it, is likely an M2 Female. Her brain was likely exposed to testosterone from adgacent fetuses in the womb and thus was androgenised during this very important part of development. Not knowing this 6 years ago, i neutered her just after her first heat so she had very little exposure to female sex hormones. What happened after I neutered her was fascinating. Within weeks, this female bodies dog started humping other dogs, raising her legs to urinate, competing with other males over females and getting incredibly annoyed by the attention of males. I let you be the judge of whether she is trans or not, she has yet to come out and ask for different pronouns so i'm working under the premiss that she doesn't care.