Currently only Github Owners can access the Context page.
The documentation is not really precise:
Organization Membership Needed
To view / edit this page, you must have an organization member with push permissions on GitHub.
Currently the only way I managed to have it working is with users having “Owner” credentials.
This is a problem since in our case (and probably many other companies) owner credentials are owned by the CTO that does not work directly on the project. He delegates the Credentials and Config Management (via env-vars) of specific applications to developers.
Using contexts is limited only to those who have Owner credentials… that is a bit limiting.