being able to see beyond surface was her best quality!

I wouldn't call her non-judgmental though.

Like AudreyFreak said, Belle does pass judgement quite a few times throughout the course of the movie, so she starts off being "kinda judgmental" and then "learns her own lesson, too" ---about how judging others prematurely clouds one's perspective, and makes it just that much harder to show empathy.

She is selfless and sensible, though.

i think she expresses an educated view rather than judgement and since she was non-judgemental, she could see past the layers of anger and spoiled behavior of the Beast.

I certainly wouldn't call Belle non-judgmental at all since she very accurately judges. Also I don't see judgmental as a bad thing since everyone makes judgments all the time, almost every minute, especially the more responsibilities you have then the more judgments you will have to make. She very accurately judges Gaston as being "rude and conceited". In my opinion Belle has a great judge of character. She judged the beast accurately too by saying he was "mean and needed to learn to control [his] temper", she was just smart enough to re-judge him after he had showed he changed. Belle never judged "prematurely", she judged appropriately after seeing actions of a person and determined who they were. If they changed then her judgment changed along with them. She never "prejudged" anyone because that would mean she judged them before having any information or real knowledge of them.

i believe a person who is able to review his own judgements are called non-judgementals as their views and opinions are not set in stone and neither are prejudiced. The fact that she was so open to do so, with someone as bad as Beast definitely makes her non-judgemental.
Personally, i'd have never been able to change my impression of someone as crude and mean and abusive as Beast, not just once but many times. In fact, i have literally learnt this quality from Belle and i;m way more open about others than I was earlier and is always willing to change my judgements of past, in context of present.

^That's very confusing because it goes against the dictionary definitions of "judgment" and "judge". Judge means "to form an opinion about (something or someone) after careful thought" & judgment means "the act or process of forming an opinion or making a decision after careful thought". In America, that's why we call our judges "judges" etc. because they are taking lots of careful thought and consideration into their decisions. Nothing about the definitions of judge or judging or judgment has anything to do with "set in stone" at all so I don't see how that's related?

because judge's statements are required to be considered as "truth" and not just opinions. I'd also like to know what would be the term/adjective, according to you, that aptly describes her this quality. Since i think we seem to agree that she could see past people's outward appearance.

Also gentle and well-mannered.