FWIW there was a discussion on here years back about how the butyrate bobbins, being softer, actually changed the geometry of the coil depending on the tension as it squeezed the bobbin in a bit changing the shape of the coil, and it made a perceptible sonic difference, though only certain discerning players would notice the difference.
Yeah, I remember many of those discussions. Thing is, the butyrate used for injection-molded bobbins, while "soft" compared to plastics like ABS & polycarbonate, isn't really so soft that it deforms heavily under tension, especially with a structured "core". If it did deform easily, it wouldn't have been good for winding coils on in the first place.
Butyrate *is* more susceptible to deformation when exposed to high temperatures, so you generally can't wax pot butyrate bobbins quite as extensively and aggressively as with other bobbin materials. That's probably the biggest reason some people hear a difference, but it's less to do with the material and more to do with what is happening in a lightly potted coil vs a heavily potted coil.
While butyrate bobbins do tend to warp and shrink a bit with exposure and time, how much this can effectively alter the overall "coil geometry" is highly debatable. I suspect its virtually immeasurable and largely meaningless in terms of actual "tone". I suspect standard production tolerances, even among newer pickups, play a much bigger role in small differences people tend to perceive between otherwise identical pickups.
Ultimately, when you compare older vs newer pickups, there are usually WAY too many additional variables at play to worry about bobbin material specifics, unless striving for "vintage accurate" construction.