There are several different types of anthropomorphic characters in fantasy. By specifying that you cannot have breasts, you know which kind of lizard you're playing.
Protagonist characters in my story don't have a gender, instead, you can change either your pronouns or your set of genitalia. Depending on your definition of gender, this should work for you. If you're having an issue with this, please let me know. There may be a bug impacting your gameplay.
You can't change race because I am a single person, and writing variations for a half-dozen races would be too much of a burden for me to perform at this time. I'm still trying to get good at just writing with 3 (pronoun sets) times 4 (genitalia option) times 2 (breasts options), 24 options in mind! Though it is easier to (and I do) break these options down into constituent parts (tail v. no tail, for instance), I simply cannot at this time afford the time to allow multiple race choices while maintaining a viable product.