I have a git repository (and working directory) that is stored in my Dropbox so I can move back and forth between computers without having to commit or stash (read: without any
The fact you are using Macs is relevant - the Macworld Hints article mentioned in a comment explains the issue (but read down to the comment that explains how to fix permissions with chmod u+rwX
etc, rather than absolute permissions that may mess things up).
This Dropbox Support answer explains what's probably going on and how to fix it - related to how MacOS X Leopard (10.5) changed the default usage of ACLs.