I have a Frontend build with Mapbox GL JS and would like it to access a private Tileset that I uploaded to Mapbox Studio. However private Tilesets can only be accessed with secret Tokens and Mapbox refuses to work when initialized with those.
Is there a way I can keep my Map private and access it through Mapbox GL?
I think you are mistaken. Private tilesets can be accessed by any token from the same account, as per the documentation:
So, switch to using a regular public token and it should work.