the question of changing ethernet cables

There are many comments here that fibre avoids EMI/RFI conversion altogether. Conversely some very experienced members prefer Ethernet avoiding the media conversion to fibre. I concur with @sns that any streaming solution is unique, depending among others on the quality of the incoming signal, quality of modem and router as well as their power supplies, EMI/RFI intensity of the location, quality of the cables as well as the receiving port implementation, noise rejection quality of server and dac and and and…l

In my experience using isolators on both Ethernet and USB resulted in significant quality improvement, that said YMMV

@finnlove 

From your description I would guess that the problem actually stems from your router: do you use it for wifi? Can you turn wifi off? Can you use a linear power supply for the router? What model do you use; can you try to upgrade? Also try a Lan isolator, my preferred solution is Pink Faun. Alternatively EMO or Acoustic Revive work well, too. 

RFI/EMI does normally not result in white noise since it happens at much higher frequencies and modulations at that frequency range would be very weak. More likely this is noise coming from the router‘s power supply.