Supporting authentication via Github as an OAuth identity provider in Wikimedia Gitlab would allow tying Gitlab accounts to Github accounts in a reliable way, which would allow things like importing patches (see T325106: Import Merge Requests from GitHub read-only mirrored repos into GitLab). See Gitlab documentation on Github login and external login in general.
There are two ways to configure an external login method in Gitlab: as an SSO (in which case it will act as an identity provider and logging in with your Github username will result in the creation of a new Gitlab account with the same name when you do it for the first time) and as a secondary authentication method (in which case you need to create a Gitlab account first, and then you either need to manually associate it with the Github account in your user preferences, or you need to use the same email address if Gitlab is configured to allow that). Wikimedia Gitlab already integrates into an SSO system, and you can't have two SSO systems (not without serious self-harm, anyway) so we'd want to use the non-SSO approach.
T215046: RfC: Use Github login for mediawiki.org has some generic considerations about the security, privacy and usability aspects of using an (optional) third-party login.