Please don't use bug reports for authentication issues. They are almost always configuration errors from the user rather than issues in the plugin.
The Jenkins users mailing list is much more helpful with authentication issues, since there are many more people reading the Jenkins user mailing list than read the bug reports for the git plugin.
I regularly test private repository access to BitBucket, GitLab, GitHub, and Assembla repositories from Windows and Linux machines using both https (username / password) and ssh (private key) based access to those repositories. It is a standard part of the automated tests I execute regularly as well.