Chaotic Good

Such as the Antihero, the Rogue, the Traitor, and the Traitorous Ally.

Chaotic Good is an alignment consisting of roles that fight in the name of good, but have opposition against the government (normally a corrupt one or one they perceive as such) and its regulations. Therefore, Chaotic Good will reject the government and attempt to either directly fight it, change it, or work from a distance in order to fix it, such as by leading or becoming a member of a group of like-minded people willing to fight against the government. Chaotic Good are also against any rules that impose on the freedom of people and believe it is wrong to limit what the spirit can do. This is why they can be seen revolting against the law in the form of Hippies and Freedom Fighters. As to be expected, Chaotic Good directly compete and oppose Lawful Neutral since the latter is embodied by authority figures who create what Chaotic Good stand against.

Good
Chaotic Good, being Chaotic, are incredibly unlike Lawful and Neutral Good, similarly to how Lawful Evil are vastly different from Neutral and Chaotic Evil since they are Lawful. Chaotic Good rarely work on the same team as Lawful Good as they are roles that would prefer a loner lifestyle, but the two alignments can function together for obvious reasons.

Neutral
Where Chaotic Good are believers of pure freedom, Lawful Neutral are advocates of pure order. The two trying to agree on most topics is like trying to marry battery acid to drain cleaner: it just won't work. Chaotic Good can't get along with Lawful Neutral because they create and enforce laws that restrict people's actions while Lawful Neutral can't get along with Chaotic Good since they act against those laws too much and refuse to listen to given orders.

Chaotic Good think of Neutral Neutral as people who are being oppressed by authority but have decided to not fight back, so Chaotic Good must take it upon themselves to act on their behalf as well as their own. Chaotic Good might try to contact Neutral Neutral and "wake them up" with Conspiracy Theories, but the only reaction they invoke from the other alignment is often ridicule.

Evil
Because Chaotic Good is a Good alignment, it is opposed to the ways of the Evil ones, mostly Chaotic Evil. Potentially, Chaotic Good can come closest to agreeing with Lawful Evil who reject the restrictive ways of the world and have decided to revolt in their own way. Bulliesundefined, for instance, don't follow the rules in school and pick on other kids while at least partially staying off of the teachers' bad side.