I often wonder how much of a bubble we live in regarding all of this. It's clear to me that City, whether they think they should condemn chants or not, are simply not prepared to play the "Liverpool game", which basically involves having to apologise every time they get upset. I also wonder how Klopp can take legal action against thoughts, as I've seen nothing official about him being xenophobic.
But about the bubble - I think the tide has turned somewhat. Ask fans of all other clubs who they would back in this situation - I guarantee the vast majority have had enough of a certain fanbase too, and they're not even involved in all of this.
Nevertheless, the Liverpool media is too powerful, and their fanbase too large, for this to die down in the near future. I look forward to club apologies the next time any fans sing something nasty or any grafitti is found. That's how it works now, right?