Well lets see the Shiekah dwell in shadow, the Twilight realm is nearly a shadow realm, the bit of light could possibly reflect something of the Gerudos...so im gonna go with they look like that because of their realm.
Now we come up to a theory I just made with a bit of info I just read. Zant also had the Gerudo symbol on his cloak, so I think the Dark Interlopers may be the offspring of the Gerudos and a few Shiekahs that went astray.
Isen't it well known that they were also hitmen though? I don't see them as being some form of Dark Interloper though, as its true they dwell in shadow their protective not evil.
I like your theory but theres one problem with it, and the only reason I know this is because I read up on the Sheikah before I started writing. It was not the Shiekah who did the betrayal but the Royal Family that turned on them. Which caused a great sorrow and is why the tear drop was added.
Nope, not at all haha, I see them as two entirely different tribes which they are, Dark Interlopers wanted the Triforce for power, while the Shiekahs job is to protect the Triforce.