Answer is here: https://stackoverflow.com/a/32088143/13346162
You need to pass the -A (as per the man page it - Enables forwarding of the authentication agent connection. This can also be specified on a per-host basis in a configuration file) in you ssh string.
You will also need add your ssh key for agent forwarding (on the machine which can access the git remote which I assume be your localhost)
ssh-add -K ~/.ssh/your_private_key
Something like this
@servers(['web' => '-A user@domain.com'])
@task('deploy')
cd /path/to/site
git status
@endtask
Git remote commands should now work.