She does nothing likable on-screen IMO. Sure, she doesn't care about social status but neither does Ting-Ting. Ting-Ting's unwillingness to run away with a soldier doesn't make her snobbish or classist. Ting-Ting is willing to sacrifice her happiness to save the lives of many Chinese people of lower status, Ting-Ting recognices her obligations to her subjects. It's not snobbish or classist!

Yes, you can also say that Mei is endurant and not materialistic because she was willing to run with Yao which means material losses for her. But maybe Mei just was impulsive and didn't realize the consequences of running away with Yao and/or she simply idealized the life of the Chinese commoners.

However, independence and rebelliousness can be good things when they are combined with caringness. The bright side of these traits can be protection of those who suffers from predjuices. Maybe in the first movie Mei would sympathize, protect and respect Mulan before her father honored her and be against that terrible.Maybe... I don't like anything she does or says on-screen IMO.