What happens when you have a Purity Sue, and remove the Purity part? You get a Neutrality Sue. This one, much like the Anti-Sue, is not afraid to be flawed. In this case, however the distinction made is not that the character is trying to be flawed, but that any flaws are Hand Waved by them being neutral characters. But, here's the interesting part... this means they have license to do anything. Want them to save a kitten from a tree? They can. Want them to kick the kitten in the very next moment? They can, with no contradiction of character.
In terms of personality, this trope usually is either devoid of emotion, or varies from deadpan to emotional to outright unstable. The Neutrality Sue basically thrives on being somewhere between extremes, and thus able to do everything in between.