I don't know what stage you are talking about, KB27787. I think someone could be pulling your leg or the information is obsolete. I've played a game on Immortal where I captured and razed every city and at no time did the CS all go to war with me.
Let's face it, I'm a DoW-happy fella, and yet, as long as I don't DoW more than one CS, by T150 I have usual led allied all the CS. I'm reminded of the words of Patton, who said "In this country, they love a winner, and will not tolerate a loser." CS LOVE warmongers, really.
Once you irritate, harass and bully City-States enough, they will all join their forces and declare permanent war against you, in which they will never stop - unless you conquer them, of course.
not sure if nukes have anything to do with it but it seems if you hit CS units with nukes for example...
Then there's the final stage where I've never seen myself but only read of is permanent war (in which you are automatically at war with all CS because they all are so afraid of you)
What about conquering city states. If for example you DoW their ally in order to not DoW the CS itself. Will you still get the "wary" penalty if you conquer?
Yes, all city states that know about the crime you've committed will decay at double rate, and you will no longer get gold gifts when you meet new ones.
I tested this by capturing 3 CS, during wars against their allies. The other CS didn't bat an eyelid.
it's never worth the trouble to get twenty units on the CS borders - it's just easier to steal a worker
2 DOW isn't too bad as generally it makes just 2 other CS wary.