Given the evidence, we believe that The Order has been influenced by a Sheikah entity that ended up on Earth ... and here's where s**t starts to get weird.
Let's start with the shocking similarities in their religions. The Sheikah and The Order both serve goddesses that died and promised to return, both try to get said goddess to do said returning by way of psychic chicks, both of whom have apparently been advised by the same stylist that white robes are the in look for today's medium.
Then there is the resemblance between The Order's symbol (the Halo Of The Sun) and several symbols in Zelda. First, let's take a look at the Halo Of The Sun itself:
The first thing that catches your eye is ... er ... the eye. Looking at you. Judging you. It knows what you did and is both disgusted and impressed. An eerily similar symbol is often associated with Zelda's Sheikah, appearing as their insignia on items such as Gossip Stones and the Mask Of Truth: