Do router and ethernet cables affect sound quality?

You might need a more transparent system, or maybe in your case there are no differences.

I mentioned earlier one test I do, 1:10 into the tune Dreamer by Sopihe Zelmani (from the collection Decade of Dreams), she sings far to the right. The position of that song is way to the right of the right speaker, and very sensitive to changes in HiFi. If I remove my ethernet-fiber for isolation that songs moves 3 dm closer to the speaker (with fiber its 7-8 dm to right of right speaker in my room).

But tests like this depend a lot of how well treated room you have, and how well setup (synergy etc) your HiFi is.