Is Buddhism about being less "sensitive"?
The effect that the emotion has on you to evoke an immediate reaction has reduced. But you will still feel emotions normally. You start to see emotions as a part of the whole play of things. They come to pass, when earlier you just reacted to everything. This is a sort of calmed reaction to any emotion. Having said that, Buddhism is sensitive in that it has compassion in it which is something like how Jesus said, "they know not what they are doing, forgive them", when he was being nailed to the cross. He was able to forgive them even as they were doing that horrific thing to him. That is compassion.