A druid can only assume the shape of a beast. Any combination of two animals would be a monstrosity.
Beasts include “all variety of ordinary animals” (MM p. 6)
while “Monstrosities are monsters in the strictest sense—frightening creatures that are not ordinary, not truly natural.” (MM p. 6)
Even more to the point, later on the same page:
Some [monsters] are the results of magical experimentation gone awry
(such as owlbears).”
A magical experiment to combine creatures results in a monstrosity not a beast — and thus would be an invalid form for a druid to assume.
D&D rules follow a classical definition of “monster”
Back in Classical Lit they taught me that the Greeks considered things “monsters” that did not fit into proper categories, that is, they were “neither fish nor fowl.”
Many of these classical monsters are represented in the Monster Manual and they, indeed, are all classified as Monstrosity.
If we look through the Monster Manual, all worldly creatures that are combinations of multiple kinds of natural creatures are classified as Monstrosities: centaurs, chimeras, cockatrice, griffons, harpies, hippogriffs, manticores, medusas, and sphinxes.
Not all hybrids are monstrous, magical hybrids
Natural hybrids (such as mules or hinnies) are a different case entirely. A druid would simply need to have seen such a hybrid to assume the form.