it depends on mainly 2 things
- what you want to see
- when you want to go
we went there in June so if you mainly go on the ring road and not planning to go out of it, then there is no need for a 4x4. If you want to do any special trips it might be that without a 4x4 you won't be able to go. For example our road to Latrabjarg if it rains you can't pass by a 2WD or at least this is what the owner of our hostel told us.
so, it is basically up to you, you can enjoy Iceland for sure with a 2WD but if you want to go off-road...might be safer for you to get a 4WD.