A thumbs down is also non-aggressive. The middle finger is escalating and can be considered provocation. Thumbs down is just an expression of disapproval. It's less inflammatory and cuts deeper.
My wife and I both use the "thumbs down" method. It's funniest when we're both doing it to some ass-hat, while riding together.
It often de-escalates the person though, as if they don't know how to respond. They usually just make angry gestures and mutter (probably obscenities) to themselves, but their rage usually chills out a bit. It's almost like you make them aware of how childish they're acting