I love critters!

I have three dogs (two Border Collie mix; one Labrador Retriever mix) and a Calico cat. Two of the four are foundlings, so I can't really say that I chose them because they fit my personality.
Regarding animals being sensitive to human gender, I got my female Border Collie, Rachael, at the Animal Shelter. At the time I had been on HRT for a couple of years, but I was still presenting in guy mode and when told the young woman working at the shelter that I was interested in Rachael and would like to take her for a walk she said, "Oh, I don't know, Rachael doesn't like men". I asked her to let me try anyhow, and so she reluctantly let me into the holding cage--while holding a can of pepper spray at the ready. To the young woman's surprise Rachael came right up to me and started loving me up and she's been my dog ever since.
On the other hand, although Rachael has always seemed to mostly afraid of men and not women, there are also exceptions, and I've noticed that the few women who freak Rachael out tend to be those whose expression is very animated and who make quick moves with their bodies. Likewise, Rachael is okay with a few of my guy friends, but only the ones who don't make violent, sudden movements or carry themselves in a *large* way, so I really can't say if it has so much to do with gender as it does with simply how a person projects themselves.