They make predictions, which can be falsified. They even make different predictions---Scott Aaronson agrees that WF poses problems for the standard Copenhagen interpretation. Sean Carroll is on record somewhere saying that e.g. objective collapse models predict an in principle measurably different evolution of a system's entropy than many worlds.
I suppose I should have asked what predictions SD actually makes.
Copenhagen Interpretation and MWI don't make different predictions from each other, but there are other theories that do. For example, pilot-wave theory makes different predictions. There are also some superdeterminist theories that make new predictions (Gerard T'Hooft is one advocate of such theories, I believe). Unfortunately I don't know of any concrete examples. Here is some more information on the subject from Sabine Hossenfelder:
I suppose I should have asked what predictions SD actually makes.