The difference is, string theorists are trying. Everyone knows that it is a major problem that we cannot currently design experiments to falsify ST or other quantum gravity theories, and everyone is working towards it in the hope that one day we may. When it comes to interpretations of QM, there is not only nothing on the horizon, people don't even speak in these terms. No one is insisting on falsifiablity, and indeed every new interpretation seems completely hell-bent on just providing a "story" around the equations in a way that does not - and fundamentally cannot - make any predictions that contradict basic QM. I can count on one hand the number of interpretations I can think of that make experimentally testable assertions, and for those I have plenty of respect[1]. But the majority of interpretations and their proponents seem to deliberately stay within the comfort zone of non-falsifiablity, writing paper after paper whose actual impact on either physics or philosophy can be summed up with "yeah well, that's just like, your opinion, man". I did my MSC in physics under a professor who is a well-known proponent of MWI (though my master's thesis was not directly related to the subject). Two years of working side by side with him proved to me that the detractors of work on interpretations are, by and large, correct in their assertions about the proponents of them.

[1] There is this one theory whose name I cannot remember, where each particle in the universe gets their wavefunction multiplied by a delta function or very thin gaussian at random intervals, and whose sudden localization also causes a sort of chain reaction and localizes all particles it is entangled with. This theory is interesting because it helps set a (statistical) limit between microscopic and macroscopic interactions; basically, when you go past a certain number of entangled particles, everything will be well-localized virtually all of the time, but for small numbers of particles we'll see quantum phenomena. Unfortunately I recall this theory having too many holes, and perhaps it has already been falsified, but the point is that at least it made an effort to address inherent problems in QM (namely, wavefunction collapse) in a way that physicists actually should; by making testable claims.