[denethorthefirst]

Beorn is the exception from the rule, he is an enigma like Tom Bombadil. The essentially unexplainable existence of Beorn does not mean that every human in Middle-Earth possessed the ability or the potential to shapeshift. Luthien is a children of Iluvatar and as such not able to change or "transform" her hröa. But: maybe she took the fur of Thuringwethil, worked some spell and wore it like an animated suit. That way she "transforms" and is able to fly without really changing her hröa (under the suit she is still Luthien).

The question remains if and how much of Tolkiens writing (like the Lay of Leithian or HOME in general) is actually "canon". If we accept the Lay of Leithian, then powerful Elf-Lords like Felagung obviously possessed the ability to change their hröa or the hröa of others in small (non-fundamental) ways (length and shape of teeth and ears, etc.). The change in skin-color on the other hand was achieved via make-up/face paint. All in all a rather miniscule change that doesn't alter the hröa in a fundamental way. In my opinion it would be a stretch to call Felagunds lengthening of ears and teeth "shapeshifting" and i don't think that this instance can compare to Luthiens transformation/appropriation of Thuringwethils body.