How can one use Binder (mybinder.org) with private Github repositories?

Question

After reviewing this exact issue (https://github.com/jupyterhub/binderhub/issues/237) it seems that the functionality for this has been implemented with this merged pull request

Answer 1

The 'Binder (mybinder.org)' part of the OP's question actually refers to two things.
MyBinder.org is a public BinderHub. The issue referenced is referring to Binderhubs in general, i.e., the 'Binder' part of the OP's question. They have set it up and documented how to enable working with private Github repositories on privately-hosted Binderhubs not via MyBinder.org. See the changes referenced by 'docs for private repo access' here.
The discussion in the issue referenced says they won't be allowing that for MyBinder.org.

For access to private repos, you can deploy BinderHub, the software that powers mybinder.org, yourself, or use repo2docker, the tool that turns a repository into a Docker image that will run on Jupyter if you only want to use it locally instead of running a service.