This is a complicated question, and shows the difficulty of applying real world scientific terms and ideas to fantasy settings. Are Owlbears, Pegasi, Hippogriffs, and Griffons mammals or birds? Are Chimeras mammals or reptiles? Do Druids classify animals in different categories like this? Since Orcs/Elves and Humans can produce fertile offspring, are they all the same species? Or are they just different species that close enough to interbreed? Or are their genetics magical, allowing them to breed with a vast array of different species (like Dragons and Angels/Devils can)? Or are they just a very complicated ring species? Do species still mutate and evolve over time? Does DNA even exist? Like others said, diseases could be caused by something else in D&D (miasma, bad odors, curses). Germ Theory may not be applicable in D&D settings.
D&D doesn’t answer these questions. Magic makes things a lot more complicated. I’m not sure these questions can, or need to be answered. It’s fun to think about, though.