I always send them. I always like to know what the pluses and minuses are. It really helps with culture victories. Plus, my goal is to limit the red faces to one. That is usually doable.
If you've ever looked at each AIs relationship with every other civ in the game, you will see that they all pretty much hate everyone else. So, it's not only you getting denounced all the time. Everybody gets it from everybody.
Also, as it currently stands, the second you capture a city you will be branded a warmonger. Because, at that point you are no longer on the defensive. Even if they surprise declared on you. What I've done in past games is to lay waste to their troops, and then start bargaining for them to give me cities when it comes to suing for peace. You'd be surprised how many cities you can get that way. That way you gain cities without the overwhelming penalty.