In fact, Iceland will be welcoming travellers irrespective of their vaccination status. The government has expressed, "No disease prevention measures will be in place at the border, regardless of whether individuals are vaccinated or unvaccinated.”
Earlier, travellers to Iceland had to carry their proof of vaccination completed within nine months or show proof of a booster shot. The government has also decided to remove all limits on social gatherings along with doing away with the quarantine requirements for people who test positive for the virus.
After Iceland, Israel is also planning to welcome unvaccinated travellers from next month. On the other hand, France is waiving all pre-departure testing requirements for fully vaccinated travellers.