If you allow someone to manipulate you, then it is not manipulation, but a game or seduction, or whatever you want to call it.
I understand your question though and… yes quite often I allow it. The reason I allow it, is to not hurt someone else unnecessary, or because the manipulation is benevolent.
Sometimes my kids try to manipulate me and my wife. We sometimes let them get away with it. It is part of life.
For instance: during dinner, one of my children may start talking about his day at school, how tiring it was and how he feels not so hungry because of that. We allow him to get away with that, even though we know it is a kind way of saying he doesn’t like the food.
One of their other food tricks is:
“Mum, the food was splendid, truly lovely, but I couldn’t eat one more bite.” (While we know it is something they don’t like, from the way they have been eating. They use this mostly when we have guests.)