You are on an island, not in it. Surely my parents are on Uist makes more sense than in Uist?
I guess that an island is kind of like a ship. You sail in a ship, not on it.
I guess it depends on the size of the island. When I go to Harris Crab House to buy oysters, I say, "I am going to buy oysters on Kent Island".
Absolutely not, i would never say on Uist, not would i say on Ireland or on Britain. It's in. Always has been.