I thought you might be
Novaya Zemlya, maybe?
I am a continent's outermost point,
Before the Soviet's annexation of Frans Jozefland, this was the Northernmost point of Asia/Europe
an island pair by a rough strait made disjoint.
Novaya Zemlya consists of two islands, separated by a very narrow fjord
Once held by natives, a land owned by right,
It used to be inhabited by Nenets, a tanned eskimo-like people
My population is now mostly white.
The majority of inhabitants are now (Caucasian) Russians, old military personnel
Named after compass points, "new" just in name,
Not sure about the compass points, but the name translated to 'new land'. EDIT: The two islands are named 'Yuzhny' and 'Severny', Russian for south and north, respectively
a nearby sea's named for a Dutch traveler's fame.
The Barents Sea, named after Dutch explorer Willem Barentsz
Cold polar water brings chills in my mouth;
The islands are deep within the Arctic circle
most of my residents live in the south.
The largest town (with the majority of the population), Belushya Guba, is located on the southern island.