Since Tolkien put people riding on giant eagles in his books (or maybe even before that), the imaginarium of riding the winds on the back of magnificent birds has generated a plethora of images and other media.
But one thing I see, is that the positioning of the rider atop the bird changes a lot. Sometimes it is over the wings, sometimes it is over the neck, sometimes even behind the wing articulations.
Some of these are not ergonomic. Not for the rider, much less for the bird.
So, I have to ask:
If we have humanoids riding eagles, where would they sit? Would it even be on top of the bird?
What would be the saddle's designs? Where on the eagle would the straps go?
Tech level is what we have here for the early XXI century. Kevlar, Teflon, Nylon, 3D printing, carbon-fiber, plastics, whatever is required for making it work.
This is science-based, but only for the ergonomics. The basic assumption that there are giant birds humans can ride on is presented as postulate.
Also, I'm not concerned about using them for war, so they do not have a use as cavalry. Just transportation / sport. It is a modern setting, people ride giant eagles for sport, not war. Versus smart drones and supersonic ammunition, it is no use to fly a giant bird into battle.