The short answer / 01
2WD is genuinely fine for a summer Ring Road loop
If your plan is Route 1 plus paved detours like Golden Circle, South Coast, and Snæfellsnes, roughly May through early October, a 2WD is sufficient and cheaper. A 4WD adds comfort and confidence but isn't legally or practically required for that scope.
When you need 4WD / 02
F-roads change the answer completely
Any F-road (highland interior tracks) legally requires 4WD, and rental insurance is typically void if a 2WD is taken onto one. If any part of your plan touches the interior highlands, book 4WD from the start.
Insurance / 03
Gravel protection matters more than the drivetrain
Chipped windscreens and paint damage from flying gravel are the most common surprise rental charge in Iceland — standard collision damage waiver does not cover it. Gravel Protection (GP) insurance specifically covers headlight, windscreen, and paint damage from stone chips; it's worth adding regardless of 2WD or 4WD.