How do you figure that? The biological classification of breeds has nothing to do with that at all. Merely what we call infraspecific taxa of domestic animals instead of races as we do humans - when both mean the same thing.
https://en.wikipedia.org/wiki/Breed
"that distinguish it from other organisms of the same species"
The truth is you just want an excuse to ignore the data and so tried a strawman.
https://en.wikipedia.org/wiki/Race_(biology)
"of
interbreeding individuals within the same species,"
Actually its you using race that implies interbreeding and therefore racism in your world. So argue against yourself.