Do characters always have to be realistic? No, and yes.
No, they don’t have to conform to ‘irl’ realism. You can have characters with horns, scales, wheels. Your characters can have the ability to fly, eat toxic waste or come back from the dead. That’s the joy of fiction.
However, if your flying, horned, toxic lizard-man exists, he needs to be justified. If he is special, how did he get like that? If not, what environmental factors do you now need to consider?
Do your harpies roost like bats or chickens? What do centaurs eat? If your Minotaur has to dress himself, how does he pull a sweatshirt over his head? And so on.
Phillip Pullman is a great example of how the physical characteristics of his creations force the world around them and vice versa. The mulefa have wheels because of the trees, which have roads passing between them because of the wheels, which have forced the evolution of the mulefa’s claws. A great circle of life.
Of course for us Fantasy writers we have a few creatures expected to turn up. Elves, dwarves and goblins are the staples of Epic and High / Sword & Sorcery tales. But have these character-creatures been done to death? Maybe, if all one does is transplant Tolkein’s elves straight into a new story.
For me, originality is what keeps me reading, but I also like to have it explained. Hence why I recently bought a copy of the superb book The Ressurectionist. Aside from the dark and gripping story, the book contains ‘plates’ of the internals of various mystical creatures. This doesn’t mean a writer has to (or even should) copy them entirely, but by consider the actual bones of your creatures, you will add more meat to your story.