So, DnD people and character creators often use a 2D scale :
1) The Good to Evil scale
2) The Lawful to chaotic scale
If the scale (1) does not need a lot of explanation,
it downed on me the the scale (2) can be seen as imprecise/imperfect.
Indeed, let's say you are talking about "altruistic monk Bob".
-> In an imperialist and repressive empire, Bob should be "Chaotic",
from his beliefs alone.
-> However, in a peaceful utopia, Bob should be "Lawful",
because there is no reason his belief might contradict the laws.
This is why I feel like the The Lawful to Chaotic scale,
is dependent on the setting and thus is not a true character trait.
Of course, a character might mostly be in one setting...
Then, I think it is interesting to consider a
"critic of law - indifferent to law" scale.
Basically : Is the character using its wits and belief to analyse laws ?
The idea is : (not) believing in laws because they mostly (don't) suit you
is not the same as
(not) believing in laws because they (don't) hold the society together.
In the end, I thought this concept should be a good discussion theme.
So, let's talk about what's defining a character, together.
Amusingly, the lawful/chaotic scale is somehow both clearer and more confusing in French. You see, the word used for lawful is the same as the one for loyal, so it can be interpreted as both being a good follower of the law, or just someone who will always remain true to his word/beliefs and can generally be trusted to act in a similar manner when two situations are mostly the same. Since that's how I've learned it, I've pushed that way of looking at it in English too even though lawful doesn't technically include the latter part, simply because "follows the law or not" is far too vague and pointless since moving to a different city could switch a character from lawful to chaotic, but including loyalty to beliefs/self-given rules into the mix makes it a stable trait that means something even if it also makes it more vague at the same time. It's kind of a contradiction, which makes it even more amusing from the irony of making the word less specific, but the meaning itself becoming something more stable and, in a sense, more specific because of it.
From there, chaotic becomes the disorderly meaning of doing whatever you want whenever you want with no shackles from beliefs or attachments rather than just being a criminal, which sounds truer to the meaning of the word "chaotic" compared to simply not following the law.
With that little bit of trivia out of the way, I approve of your idea of moving to critical/indifferent to law for the sake of clarity, but I'd like to point towards a different and larger grid I've found online a long time ago. A 5x5 alignment chart that uses the following:
Those simply add the missing categories that would be awkward to place in the usual 3x3 chart. The good person would be a paragon of virtue, but a moral person wouldn't be opposed to doing evil for the sake of a greater good, while the corrupt wouldn't be malicious but only work for personal gain at the detriment of others if necessary, compared to evil who just enjoys watching others suffer. Comparatively, the lawful→chaotic scale becomes far more complex, as the lawful would strive to follow the laws of whatever place they are in no matter what, while the social would do whatever makes them accepted by society, which tends to be lawfulness but can sometimes branch out into non-lawful if society sees the law in a bad light(under dictatorships, for example). Rebel is where your altruistic monk example would come in, it might seem weird to have him closer to the side of chaotic, but rebel shouldn't be seen as an in-between neutrality and chaos. The rebel is someone with a fixed set of beliefs unrelated to any society. They will be lawful in a society of similar values, they will be criminals in one of different values, the point is, the rebel has fixed morals they follow religiously and no society or law will change that. And finally chaotic which is exactly what it says on the label, do whatever, whenever, because you feel like it or some other arbitrary reason like "it would be funny".
I honestly feel the 5x5 chart is the most representative thanks to the amount of variety and being more specific on what each label means, unlike the common 3x3 which either means nothing or ends up creating heavily stereotyped characters. Unfortunately, it was never used anywhere outside of some visibility in certain parts of the internet, so no widespread knowledge of it leads to it never being scrutinised or used since people would generally not recognize the added terms without a paragraph to explain them like I just did.