SSO Auth Issues
An uncommon, yet not impossible situation can arise due to SSO authentication issues with GitHub where a newly created repo, such as this open source CircleCI-Public repo, is unable to be added as a project.
Another situation can arise if the project is then added by another authenticated repo owner and then said user clicks "Follow Project" which results in a 403.
1. Single Sign-on for your org
go to Project Settings >> select "SSH Keys" >> "Authorize with GitHub" under the User Key section
Alternatively, visit your User Settings under your avatar in the lower left hand corner of the menu and "Check permissions on GitHub" under "Account Integrations.