I guess I’m in the "It’s mostly BS" camp and I’ll leave it at that…I like to be proven wrong as it means that I got to learn something. I still question burn in with cables as this suggests that they will change with use. I’m pretty skeptical on that but there are folks who claim to hear them change so, who knows.
As far as my understanding, some interconnects are grounded or shielded on one end so are designed to be used in one direction but could be wrong with that. But one day I inadvertently installed my digital cable backwards and my system sounded totally broken and I was panicked. I fairly quickly realized my mistake and when I reversed that interconnect everything was great again. I don’t know whether it was the cable’s construction or whether it had been burned in that way, but the difference was severe and unmistakable. For whatever reason, ignore directionality at your peril.