Actually I have read most of the tales of Robin Hood, not just the Disney, Errol Flynn and Kevin Costner editions. I won't say I have read the originals as no one is sure where the story originated or if the original inspiration for the stories os one person or several.
Only the later versions of the Robin Hood tales refer to him fighting the illegimate authority of John, the earlier ones make no mention of King Richard (and In fact make reference to King Edward). The Lionheart is only added later, much the same time as other tales of chivalry began to gain popularity (such as Arthur).
The earlier tales are full of examples of his chaotic demeanor.
So before we continue the discussion, we should define which version of Robin Hood we are referring to.
he does care what others think of him - Not a trait of either lawful or chaotic characters, although chaotic characters would be more inclined to not care I will admit.
does not act arbitrarily - several tales have him kidnapping people to dine with him as he doesn't like to eat alone (he would then charge them for the meal of course..); pretty arbitrary
and is not irresponsible - one version of RH has him becoming an outlaw for killing the Sherriff's men because they would not allow him in the King's forest.
he formed a whole society...how can one say that he is irresponsible or has no concern for regulations - so if you are the leader of a thieves guild you are not chaotic? I realize this is abit of a strawman arguement but I think the point is clear.
he acted consistently over time....how can one say that he acts arbitrarily - he has acted consistently chaotic.
Have to go home now, enjoying the discussion though!