The first permanent settlers of Iceland were Christians. Inndeed Iceland is one of a few countries worldwide if not the only one first settled by Christians. Long before the Vikings, Irish had setlled there, confirmed in the "Landnamssaga" the Icelandic Book of Settlement written in the 12th century...

In the year 1000 Iceland converted to Christianity by a parliament decision. Paganism was not banned but had to be performed in privacy.

Iceland has been Christian since first catholic then protestant for over 1000 years. You can easily check this fact by the number of churches around the island.