Should one put their Master's thesis online?
Every document is, in the way you define it, immature. With everything you write your writing improves. Your papers will not be better because you have a degree. They will be better, because you learned something (i.e. made mistakes) before. 

However, there might be reasons not to publish your thesis, but it is not so different from normal working papers. Maybe your thesis is just bad, you did not get any meaningful results, you have made significant mistakes, etc.

So if your university allows, publish it online if you want to (or if you think it may be worth reading / you can not think of a good reason not to); everyone knows, it is only a master's thesis and will read it in a different way than they would read a published paper (or not at all).