A character who has a Neutral alignment in regards to Law vs. Chaos finds himself in an interesting situation. In all likelihood, he generally lives his life by what methods he sees fit. If obeying the local laws tends to give him the best life, he’ll do that. If things change, so will he.
Note: This is not necessarily about greed. Rather, this is often about either not having deep-seated beliefs about freedom and control or believing that everyone should be given a choice and that choice respected and honored, though the latter option could also be possessed by a Lawful character.
A group of druids, observing a war between monks and barbarians, choose not to interfere because the war has nothing to do with them. If they later choose to side with the monks because the barbarians have been killing druids on sight, then they’re not acting in either a lawful or chaotic manner. The same is true if the druids side with the barbarians because the monks have been oppressing the peoples of the land, even if the druids are unaffected by this. If both events are happening, the druids could split along ideological lines of neutrality, even fighting each other in the war, without anyone risking the Neutral aspect of their alignment. If they chose to fight against both or if they chose not to fight, they would have those options as well without fear for the loss of their initial Neutral alignment.