In my case, OS X has the latest git, while Windows is stuck on 1.9, and my git folders get corrupted if I do a push on OS X and simply do a status on Windows. I guess something has changed between 1.x and 2.x but this corruption is really not something which should ever happen in a VCS. My solution is to use Gitlab instead of Dropbox only local repos.
I'm not aware of any changes between 1.x and 2.x that would corrupt a repo... I use a mix on various systems, some even still have git 1.7.x on them. The only problem I run into is when you have some script that depends on a newer git feature added in a newer version...
My money would be on Dropbox busting your repo somehow. I don't think Dropbox is an ideal solution for pushing/pulling git repos from.
