Posting a (non-original research) Masters thesis on arXiv?
In my field (cosmology), plenty of researchers and professors post lecture notes on arXiv, and of course many people write and publish review articles which don't contain any new results. So there's no requirement of novelty to post on arXiv.
Whether it looks immature largely depends on the quality of your writing. A poorly written review will not be read, and could reflect badly on you if you continue in academia (employers and grant reviewers will look at your Inspire and/or ADS profile). Bear in mind that you can't remove things from arXiv.
I would highly recommend asking your supervisor about this. They are best placed to tell you whether it's appropriate or not, according to the quality of your work and the conventions in your field. If you don't post on arXiv, you could consider uploading the pdf to your own website, a public github repository, google drive or similar. Then you can still share the link with interested people.