I'd say I have matured significantly in my life, particularly after dx. It took a long way, though. Part of it is to understand that you can't just have it all, you need to let some of your dreams go (not all) to have more room to your true self. Since I always wanted to be a better person and better meant 'help people and myself' I needed a better sense of balance between the two halves. Not at all easy, considering that my neurology didn't provide me with the assets needed for efficient social interactions and reliable self-reflection. Autistic survival guides (particularly that of Marc Segar's) and this forum have taught me that I can learn new social skills. It's not that difficult but it requires a lot of practicing and possibly help from a therapist/close friend.
Maturity requires taking responsibility. I think it's more important than being independent. You can depend on others still you can be very much responsible for certain important life areas of your own and perhaps of other people, too. It all have to be laid out in your mind. One important thing is to speak up and stand up more for your own good (not only rights, but everything that can make your life better). As a general rule, keep your opinion to yourself and only disclose the ones that are appropriate for the situation and are in line with your intentions. Stick to your decisions even when they are seemingly failing (to a reasonable degree, of course). Never let others to play with you or abuse you in any way, even if their actions seem well meaning. Be firm, but diplomatic, as gentle as possible.
Rationalism is overrated (in general). People are emotional beings, autistic or not. So, listen to your emotions. Try to explain them. Try to trim them. A principal rule for autistics: The better you understand your emotions the more you can do for them. You have to nourish them, meaning doing all the things people usually do as ultimately they all are motivated by the same set of emotions. The only difference is that some do it instinctively (see: NTs), others with more and more rational thinking (mostly autistics). (In reality most people are a mix of the two.)
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Another non-English speaking - DX'd at age 38
"Aut viam inveniam aut faciam." (Hannibal) - Latin for "I'll either find a way or make one."