Beware the semantic trap. There are only two (biologically determined) sexes. There are, however, countless “genders” (a socio-psychological construct). The whole idea is to make it impossible to think, or express a coherent thought on the subject. Don’t fall into their trap. Say (eg) “There are only two sexes; while the number of genders is only limited by the twisted imaginations of delusional hdeviants”. That would probably keep you out of trhouble. (NOT! Ha.)
If humans have many, many genders, then how many genders do canines have?
My 1983 Websters New Universal Unabridged Dictionary disagrees. It allows only Male, Female and Neutral (Genderless). I doubt you will find anyone referring to gender as a "socio-psychological construct" before the 1990's. Of course, if you don't the definition of a word, change it! Easy to do if you own the education system. My 2003 American Heritage College Dictionary allows unlimited options.