Two things:

1. You are not the one who is not ''mature enough'' to deal with this, HE is. He is not enforcing boundaries but instead, is enabling her and putting her before his supposed girlfriend.

2. The issue also isn't that YOU have a problem with it but that HE doesn't and, again, prioritizes her over you.

He is not ready to be in a relationship with you, that much is clear. Why be in a relationship where you are not supported and prioritized?