How can different CAT5/6 cables affect sound.

So, doing a little research on streaming, according to Gemini, they primarily use TCP, not UDP.

As  I suspected, UDP is best used for live streaming, in cases where you would rather have the audio in real time than perfect.  Consider a video call.  Can you wait 10 seconds to hear the others in the meeting? Then use TCP. On the other hand if you’d rather suffer packet losses and be able to carry on a conversation, use UDP. 

In an audio streamer the point is moot anyway as you still get bit perfect transmission from your cable modem to your streamer.  Assuming UDP or TCP.  The de-ionized, cryogenic, thrice blessed cable you use for the last 2 meters won’t change a single bit.  Besides in a bad Wifi environment, any packet losses are going to happen long before your home.

What does matter is the quality of the buffering in the streamer, and how well the clock on the DAC is able to get data when it wants it without a conflict with the input stream.  

Last post, honest.

To add to this, I live in an area where power and Internet is spotty.  One or the other or both can go out.  I use Roon for streaming.   I have a light in my office which turns on when the Internet is in failover mode to my alternate provider so I can literally watch the light and tell if I’m online or not.

The failover process however takes about 20 seconds to recognize that my primary is down before it switches over.  20 seconds.  

I’ve been happily listening to music while this has happened, and sometimes movies, without a single interruption.  

That’s how buffering works.  It pre-fetches the stream before your DAC or TV is ready for it and deals with the missing packets and broken connections in the background.  Cable quality be damned. 

The same happens when I’m driving.  I go in and out of cell service often.  So long as the song has started playing I never notice.   A much better investment is using a low noise wall power adapter from iFi to prevent the switch mode noise from polluting your AC.   I have my switch and streamer (a Raspberry Pi 5) on them.  

First of all, it's not "beyond doubt" and the answer to the initial question is, they can't, objectively.

It’s the analog signal that carries the digital signal (voltage fluctuations) over the copper Ethernet cable. 
Yes the data is transmitted accurately. However, we’re streaming music, not moving text documents over network. So in our systems the Ethernet cable is a digital cable. Just like any other cable - quality of the conductor, dielectric, shielding, connectors, etc. Everything matters for the quality of the signal received and processed by the component that’s fed by that cable. 
Your system will reproduce music just fine with a cheap cable as long as it works. You don’t need to spend a ton in Ethernet cables.
If you have a revealing system you are very familiar with, you will hear differences between Ethernet cables. I hear it in my system.