glassfish.common/src/org/netbeans/modules/glassfish/common/AdminAuthenticator.java permanently replaces org.netbeans.core.NbAuthenticator as a default java.net.Authenticator. I don't know if that's correct or not, but that's not the point.
Git support uses a 3rd-party library (JGit) for communication with remote repositories and that library handles authentication and authorization itself. But when any NB implementation of a java.net.Authenticator comes in the way, the connection (push command to be more precise) fails. For that reason we modified org.netbeans.core.NbAuthenticator in 7.1 to be capable of working with mechanisms that do not require (refuse actually) the dialog asking for username and password. Do you think you could rewrite AdminAuthenticator to work the same way?

Scenario:
1) Git runs a git command in:
> org.openide.util.suppressAuthenticationDialog(Callable<R> blockOfCode)
that sets a flag that tells the default NB authenticator to suppress the dialog and return null when getPasswordAuthentication is called
2) When getPasswordAuthentication is called, NbAuthenticator displays the dialog only when:
> NetworkSettings.isAuthenticationDialogSuppressed()
returns false
3) For a git command, the dialog is then never displayed and it successfully connects to a remote repository

Do you think you could display the dialog only when NetworkSettings.isAuthenticationDialogSuppressed() returns false also in:
glassfish.common/src/org/netbeans/modules/glassfish/common/AdminAuthenticator.java
j2ee.sun.appsrv/src/org/netbeans/modules/j2ee/sun/ide/editors/AdminAuthenticator.java - i don't know if you manage this class too. If so, please modify it, if not pass forward.
Thanks