I think the issue with the testability of String Theory is as follows:
In a theory, there are generally variables. For example, in General Relativity, there are "constants" (called such because they are measured via experimental science) that emerge from the theory. These "constants" are actually variables in General Relativity (if you were to set them to different values you would have a different "universe"). However the important thing is that "variables" that we had yet to measure which the theory predicted would be certain values (given other variables which we had measured and plugegd into the theory) turned out to be consistent with what General Relativity said they would have to be when we did get to performing experiments to confirm their values (so far).
The problem with String Theory is that there are many variables (not a show stopper) but that they seem to need to be fixed at certain values to arrive at "our universe". One might say General Relativity did the same thing, but no, given a set of variables that we had measured, we got predictions on what the values of the remaining variables in the theory must be. This does not seem to be the case with String Theory where we have not found any good reason to set the variables the way they must be to get our universe's constants out of the theory.
Why is this important? Because String Theory MIGHT be correct (i.e. more accurate than General Relativity) but we have no indication of why the variables in the theory should be set the way they are (i.e. no experiment has been constructed as far as I know that will measure a value in reality and set it to a specific value in the theory). And even if that were to happen, it seems that it is possible to fiddle with the other variables in String Theory to again arrive at the model of our universe. So it seems that we would need to experimentally resolve each variable in String Theory independently which says to me that the theory has no predictive capability.
IANAP, just an enthusiastic amateur who is annoyed at the state of physics.