Imo it should be like this:
* If you take one CS: those civs you've met will have a minor diplo hit with you for 50 turns, then forget it. They won't outright DOW you but there may be a few denouncements if the civ wasn't friendly before. If someone had denounced you before then they might DOW you.
* If someone was allied to the CS, they will hate you forever (like all civs do currently).
* If you take a second CS, you will take an influence hit with every CS on the map that will fade over time, and a more severe penalty with other civs. However, it will still fade over time, but will take something like 80 turns to fully disappear, and there will likely be at least one DOW as a matter of course.
* If you take a CS before you've met any other civs, then there should be no penalties, or very minor ones. Isolated starts need something to give you a leg up, especially on Deity and Immortal.
The numbers could be tweaked ofc, but the idea with these penalties is that you would have to weigh carefully whether taking a CS or two is worth it or not. If you've got bad land to expand to and your worst rival has allied a nearby Military CS with a useless UU, then it might well be a viable option. Otoh if quests have given you a Cultural CS ally with very few luxury resources and poor land, then it wouldn't be so wise to take it. Etc.
You could also make it so that a conquered CS is easier to flip to other civs with ideological pressure; they might remember their CS origins and flip merely in order to spite you. There are many viable changes... Imo Firaxis is far too conservative when it comes to changes like this.