Set the permissions of Non-root Users to only themselves

I am a Project Director, who needs my team to work with docker. However, we found non-root users can use docker containers as root user, which means they can access some important file mounted in container.
How to solve this question?
–user option is definately useless, as everyone can choose not to use it !

The normal docker engine runs as daemon with root permissions. If unprivileged users are granted access to the docker.sock, they can effectively use docker for permission escalation. It should be no surprise, as it is mentioned in the documentation.

You might want to look at this topic for further ideas: