Every city you take is an escalation of hate a civ will have towards you. Depending on the civ there is always a point of no return in which no civ will treat you like a legitimate partner at all. And if you have attacked most the civs in the game they will definitely not like you if you've taken multiple cities by force.
Think of real world parallels.
It would have taken hundreds of years for the European powers to treat Mongolia as a legitimate state devoid of threat and not seen as reprehensible. Same with the chinese. They would NEVER respect a Mongolian state had it survived. The Gauls, the Germans, the Celts would never just accept in a theoretical sense, the Roman Empire.
The Germans in 1942 would never again have been treated with the level of legitmacy they had in 1936. The Chinese still hold a grudge against Japan. The North and south Koreans are still at war. The French empire under Napoleon probably could never really become an honest actor in European society, even if he had stopped at his height.
Even today Russia takes ONE tiny city, in the scope of Civ, and he gets chain denouncements.
Iraq under Sadam conquers a civ and gets war declared on him
ISIS essentially "razes" a few cities and rightfully speaking the whole world declares war
So if you think about your civ in that context, think about what would be acceptable in the real world. There is always a point in which the world will refuse to interact with you. It just makes sense.
Knowing that, you have to make sure the original cities you found, have to have a diverse scope of resources to get happiness from. Build Happiness wonders. Declare war against unrespected Civs who might be weak and at war with others. Just aim at there capital and minimize the cities you take. Avoid conquering city states because eventually they'll be your only trading partners and source of resources.
If you conquer a civs capital, and wipe out their military units and pillage tiles. You basically cripple them for the rest of the game. You don't need to wipe them out.
At a certain point you WILL be hated. And it makes sense other non warmongers will want to survive. Make sure you're ready to handle that with plenty of resources under your empire.