EDIT- having re-read this, (it is a bit TLDR,) it all seems seems to come back to respect for both yourself and other people.
I think maturity has several aspects.
1 Just because I can doesn't mean I have to. (I can go to a pub, drink till I get thrown out, pick a fight with the doorman and spend the night in the cells if I choose to. (or, if that's not your cup of tea) I could go onto a multiplayer game, call myself 'Lord Todgerface' and start screaming abuse at anyone and everyone when I get my bum kicked, or hit them with a lucky shot(whenever I play multiplayer fps, it's a case of lucky shots). Why would I do either? Honest answer- I wouldn't)
2 Acknowledging that everything has a context, and you might not understand it. (That rude guy might have just had the worst day of his life. The waiter who doesn't speak English very well- he could be a student trying to pay his way through uni before using his degree make changes to his local community at home. That hipster looking dude over there may well actually enjoy skinny jeans, fake glasses moustaches and having 2/3 of his hair shaved with the top permed. As a European, despite having lived and worked in the states for 2 years, I might well not be an expert on the constitution, the 2nd amendment and why keeping dirty great big guns around the house is either a good or bad idea, but some people can give me the information for both sides, and if I cared enough, I could easily find it, but I would never be able to understand it from an American perspective.)
3 Just because I disagree with you, doesn't necessarily make either of us wrong. (My favourite car might be a 1988 Ford xr3i* painted that sky blue that most late 80's and early 90's fords seem to come in, and yours could me some kind of classic E type jag**. both are valid answers.)
4 (This is a big one for me) Respect. I bleed red, so does everyone else on the planet***, regardless of race, gender, sexual orientation, disability, mental health, age**** and anything else. As long as we all bleed red, we'e basically the same. Nobody deserves any more or less respect until they have earned it with you (either personally or through what you have learned about them- I never met Churchill, but having read a biography, I have a lot of respect for the guy.), or they're Usain Bolt.
5 Not gossiping. Now, this is one that's kinda variable. I believe that there is gossiping, and there is gossiping the former is when you're all sitting around having a round of diplomacy laughing about what's going on in everyone's life, and what's going on with different people. The latter is malicious and nasty.
6 and finally, accepting that your rules only apply to you. Nobody else on the planet has your experience. They're all going to judge maturity differently, some (like me) may have fairly long winded pretentious sounding lists of ideals, others may have more simple statements. I can (and do) judge people by my standard, but I can't expect them to keep it or think badly of them for not keeping it (still working on that one).
As I said, I know this looks mostly like a very pretentious set of 'I'm better than you because I do xyz' list of things, but hopefully nobody sees it as such*****, it's just my answer to the thread.
And I guess, it could be summarised much more simply. 1 Emotional self reliance, 2 the ability to interact with and accept different people, 3 the ability to be interdependent (with team members, partners, or colleagues) when necessary, and 4 knowing the difference between when you can do something, and when you should do something. Once again, sorry for the TLDR answer, and how pretentious it sounds.
*isn't, but might be.
**Not really a car person, but I hope the E-type is a classic, if not, sorry for looking like a noob.
***Although I once heard that the Queen was a lizardman shape shifter- not sure what colour that would make her blood.
****Not sure that my gran counts either (bless her cotton socks)
*****Though if you do, feel free to keep it to yourself.