So far I have not seen any animal that specifies gender that disagrees with the biological gender. (Someone is free to give examples).
So Kater, Bärin, Kuh specifies gender (male, female, female) and therefore takes those grammatical genders. These terms can only refer to those specific biological genders.
This is unlike the generic terms of Katze, Bär, Rind which does not specify any gender and applies to any biological gender, and will therefore not align between grammatical and biological gender.