I have a different take; pickups make a difference, but not as big as people think. Wine is complex, wine has a lot chemicals going on, there are a lot unknown data points unseen is that dark red liquid. Pickups, on the other hand, have a comparatively simple task, one that is easy to describe with basic physics. When you cross out all the stuff that makes no difference, such as the wire insulator, or the bobbin material, and focus on the physical task of the pickup, all there is to consider is the resonant peak and the Q factor of the pickup, and perhaps how high or low you're setting the pickup with respect to the strings, and the values of the tone and volume pots. Even though what the pickup is doing is simple, psychoacoustics (the combination of the heard sound with perception and bias) make the idea that pickups are very complicated seem plausible. People talk about pickups having lots of mysterious qualities, and it seems believable because of psychoacoustics. It's sort of like religion, where is something good happens, people will say it has a divine cause, because of the psychological tendency to misjudge probabilities, as well as ignorance of causality.
If you tweak an EQ pedal, you can make a the signal chain put out the tones you would get from a different pickup, and IMO, the only reason nobody recognizes that is because when you are fiddling with an EQ pedal, you know what you're doing, and you properly attribute the heard difference to the EQ pedal, and not magic (scatter winding, authentic vintage unobtanium). The physics pf pickups are not complicated, but they're still over most people's heads, so when some authority figure who makes and sells pickups talks tall tails of their researching vintage mojo, most people don't have the understanding needed to refute their BS, and so it proliferates on the internet.