@almarg
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As an electrical engineer having extensive experience designing high speed digital, analog, A/D converter, and D/A converter circuits (not for audio), I don’t find the reported differences to be either surprising or mysterious. And I consider them to be well within the bounds of established science and engineering.
Most likely what is happening is that differences in the characteristics of the cables, such as bandwidth, shielding, and even how the pairs of conductors that carry the differential signals are twisted, are affecting the amplitude and spectral characteristics of electrical noise and/or RFI that finds its way via unintended pathways to unintended circuit points "downstream" of the ethernet interface in the receiving device. "Unintended circuit points" may include the D/A circuit itself, resulting in jitter, and/or analog circuit points further downstream in the component or system, where audible frequencies may be affected by noise that is at RF frequencies via effects such as intermodulation or AM demodulation.
"Unintended pathways" may include, among other possibilities, grounds within the receiving device, parasitic capacitances, coupling that may occur into AC power wiring, and the air.
What can be expected regarding such effects, however, is that they will be highly system dependent, and will not have a great deal of predictability.
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Yup. Badly designed or faulty equipment will indeed be vulnerable to unintended pathways.
Always better to get good equipment to begin begin with rather than band aid things by finding the least bad sounding Ethernet cable !!!!!