I had a player who was annoying playing a CN in a campaign and considered booting them. The campaign ended and I decided to give them a second shot because the next character was going to be LG. You know what? Just as annoying and disruptive. Alignment on the character sheet doesn't matter, the player does.
In my experience there is little or no correlation between the two. It takes a "unique" individual who wants to play a jerk or a disruptive character. Which they justify because they're just like their favorite anime character or because "it's realistic to hold a grudge over a long-forgotten minor slight".
In other words...
- LN: "I do not care that the lord is sacrificing slaves. He is the rightful ruler of this land and he is within his rights. In fact, you are all now under arrest."
- LG: "My order says that it is so, we shall not lie or deceive to get our way. The entire party must abide by my rules."
- CG: "I don't care if the laws are just, I shall do what I want when I want for the greater good. The peace may be broken, war may erupt, but these peasants suffer under the bondage of law!"
- CN: "Me? Evil? No, of course not. I'm just stealing from the party for the fun of it."
- N: "Why should I care, it's all part of the balance. For too long this has been a good and peaceful land. Evil deserves it's turn."