MLP Gen 4 quite obviously draws a great deal from classical mythology: hydras, Pegasus, Mt. Olympus, etc.

Even Luna/Celestia are throwbacks to the way that ancient peoples thought about the world. Before modern science came around to suggest otherwise, it was often thought that gods or their helpers directly operated all the natural workings of the universe on a day-to-day basis. The myth of the hostile brothers Osiris and Set comes to mind with Celestia and Luna: every day, Osiris was thought to sail a divine barge holding the sun across the sky while his brother Set (the god of darkness, storms, and the desert) fought against him the entire way. Quite a lot of stories with that same motif: Romulus and Remus; Cain and Abel; Jacob and Esau et al.

The Changelings also arise from that same magical dawn and operate on a similar kind of logic. Although I at first thought they were more influenced by popular depictions of shape-shifting characters in science fiction media, the idea of the changeling turns out to be quite ancient. MLP changelings don't even necessarily require brains at all like the ponies would even though their anatomy suggests that they would have one. 

How can that be?

Leaving aside the obvious answer that it's a cartoon show designed to sell plastic horsies, the truth is that it operates on a kind of pre-modern concept of knowledge and cognition. From what I understand, everyone is born with a certain amount of basic mental software so to speak that would represent a bundle of inborn mental elements like instincts, personality, and so on. Quite a lot of it is a result of genetic expression, but there's an aspect of randomization to it as well via mutation and probably many more factors. Most of what an adult human knows, however, comes from sensory data drawn in from the outside and processed/stored inside of the mind. 

Shape shifting characters of the older type don't tend to work that way: most of them can't work that way, because they don't have anywhere to store information when they transform. In the olden days, the human brain was not necessarily always considered the seat of consciousness. Everyone knew what would happen if you hit someone's braincase with a rock, but that pile of mush inside wasn't really "them". The real them was what you would call their soul or spirit, and that vessel could hold information, too. 

You can call it magic in terms of the show, but it operates the same way: the changelings couldn't remember their original shapes in the sort of electro-chemical way that we utilize in our own memories, but would just have to "know it/remember it" through some other means. Ancient people wouldn't have a problem with this at all. How do faeries and woodland spirits just seem to "know" all kinds of things that human beings don't in those stories? Sometimes they are so old they have seen everything twice, and other times-most other times- it's just their nature. 

MLP changelings kinda work that way and kinda don't: we see that they have a life cycle from birth to maturation like biological entities with internal attributes of magical/legendary creatures. Their favorite nourishment of "Love" is a toned-down version of evil spirits who would drain the life force/spirit/souls of their victims for whatever reason. The comics fittingly suggest that their origin came about from a mixture of magical and natural elements which sort of fits, but I don't know if the creators had that idea in mind at the time of the Changelings introduction. Scary creatures.