You can opt-out your repositories from The Stack dataset by creating an issue in this repository and listing the repositories you would like to exclude. This will exclude those repositories in the next iteration of The Stack. You can check if any of your repositories are in The Stack with the Am I in the Stack app.
By creating an issue we can verify that you are the owner of the repositories requested for opt-out. Once your opt-out request has been processed we'll comment on the issue and close it.
Link to opt-out issue: click here.
For more information checkout the BigCode website.