A "monster" is really a malformed creature. Malformation supposes a deviation from a base population... you cannot have a "race" of monsters because then they're not monsters. If "minotaur" is a race then the only "monstrous" minotaurs are those born without bull's heads, etc.
I reject the base premise, at least as far as mythology is concerned. A great many "monsters" in, say, Greek myth, are not members of species at all, but are one-off critters. The Minotaur is a good example of this, as is Pegasus, and several other Greek cthonic monsters.