It's relevant to note, of course, that both have different creators: werebeasts were the creation of Hircine (this is quite explicit and well established at this point) while the Khajiit were created by Azura, probably from a common ancestor to Bosmer (this is according to their own myths, with relatively little confirmation or corroboration)
So, what's the connection here? And what, if any, is the connection to Lorkhan (as the moons are the remains of his "body".) Did both Azura and Hircine tap into some kind of cosmic loophole relating to the moons? Or is the "moons phase + animal form" thing just coinicidental?