There is the concept of "Island Reserves", which is basically having additional fuel so if things suddenly go wrong at your destination you can divert somewhere else. It's one thing to have sufficient for the nearest alternate, and a lesser for where is operationally convenient, ie return to start point. Care is also taken that met and forecasts are adequate. Keflavik has multiple runways so if one is blocked in front of you, there's another.
I'd always understood that the standard first alternate for Keflavik is Akureyri (I once looked down on it from an LHR-YVR flight; town was nothing of consequence but there was the airport, lit up at night). Adequate runway, opposite side of island so different met, etc. As ever, both airports have to be looking good and not anticipating unacceptable weather before you depart. Airline ops departments have been doing all this for a long time.
Bermuda flights have sufficient fuel to make it to the US mainland. Easter Island is a challenge, but the procedures are described above. St Helena has recently joined the club, the diversion is Ascension Island, which is nearer than going back to the African mainland, although the latter is operationally preferred.
ETOPS is a variant on these procedures, and any (rare) closure of Keflavik could have an impact on Transatlantic flights that normally go nowhere near it.