I'd suggest this approach.
Amongst the audiophile community, there is a very significant statistical majority that there are audible differences in cables. These are people who have done all kinds of listening tests in their home environments, and many would have preferred to not spend any unnecessary money.
These differences are statistically significant enough to comprise a valid observed phenomenon, over a disparate group of individuals.
Now, the scientific response should be that since existing electrical testing methodology has only shown minor differences,and that A/B/X testing has not determined anything sufficient, that there must be some other testing methodology found to either support or refute this widespread observation.
Case in point: When optical communications networks are used, fiber-optic cables carry the signals. Electricity is applied to one driver, and comes out the other end's receiver as electricity(of course opto-couplers are used in this case, but bear me out). If I took that fiber-optic cable and tested it for electrical characteristics, it would seem that it wouldn't even carry any electricity, and it won't. But that doesn't mean that signals are not carried on it. You have to design your testing protocol to measure what you are trying to determine. When we add in the opto-couplers and know(ahead of time) that we are transmitting light signals with couplers on both ends, then we can measure the performance adequately. Similarly, we don't really know for sure(and this whole thread bears this out) what we are trying to measure. All we know is that the existing measuring techniques are apparently not adequate to account for a statistically significant and widespread observation.
So, one way to deal with it, is to just "dismiss" it as folly, or imagination. The other way is to figure out why the tests are inadequate, and determine new tests that actually can make some headway to finding out how to measure what is so commonly observed. The first step in this is to try to determine what the cables are doing that is not in our testing.
If every scientist dismissed everything that could not be readily measured at the time, we wouldn't know anything at all. Measurements are made to quantify observed phenomenon. Anything that is a statistically significant occurrence, justifies further investigation to find tests that can quantify it, whether they be electrical tests or acoustic tests, or whatever.
Something is going on here with these cables, and it would behoove us to find out what it is, and why it is.
