You’d be fine in Reykjavik.
You may not be able to have easy access to every amazing soy meat analog product available, but there are plenty of markets that sell breads, produce, spreads, and what have you. And, last I checked, there are three vegetarian restaurants in Reykjavik as well.
But eating out is expensive, so if you can get used to cooking at home very often, and live in one of the bigger cities in the country, I think you’ll be fine. (Regardless of diet, most people in Iceland cook at home anyway.)