Neutrinos flying faster than light won't destroy relativity, just like relativity didn't destroy Newtonian physics. There's no easier way of saying that. The E=mc^2 equation (or better E = sqrt[p^2 * c^2 + m^2 * c^4], p = Gamma * m * v) will still stand. Decades of work in particle accelerators have shown this to be true.
Until this gets verified by several other detectors and thoroughly checked, it's just an interesting result that's probably an error. After all, we have plenty of examples of neutrinos flying slightly slower than light.
Wait what? Relativity completly destroyed Newton physics. Newton's equations sure do give good results, good enough that they can still be used, but they do not at all describe accuratly what gravity is or how it alters space.
And E=MC^2 is not the heart of relativity, not even close to it. If E=MC^2 was all that was important in relativity, then there would be no issue with it and quantum mechanics. E=MC^2 actually plays very very well with Quantum Mechanics, and that can be see in the coupling that occurs when two particals collide and express the extra engergy as matter antimatter pairs before the two particals depart on their altered paths.
The heart of relativity is in motion, and how it is impossible to differentiate between an object in motion or at rest. Special Relativity makes the claim that there is no physicial experiement that can be done to differentiate if a system is in constant motion or is standing still. Every object not under going acceleration can claim to be at rest. If matter can be moved faster than light, then information can be moved faster than light, and now it becomes possible to determine if an object is moving or not.
General relativity eliminates the requirement for constant motion and says that any object can claim to be at rest, by saying that it cannot be determined from within the closed system if the acceleration being felt is either from change in velocity or gravity.
Just think of the classic example of the two astronauts in deep space with giant clocks. One is at an absolute stand still, the other under going constant motion and they cross paths. The short end of it is, both astronauts will conisder themselves to be the one standing still, and they have every right to, and they can look at the clock of the passer by astronaut and the time differential they see with that clock to their own clock will verify this, but there is no way for one of the astronauts to report the discrepency to the other, because by the time the information gets to the other guy, the reverse will appear true. If you can send info faster than light, then the right each astronaut has to claim he is at rest goes out the window.