Git fatal: unable to write new_index file

Sounds like you're actually sharing the same working repo across multiple users, which is in general not a good idea:

• you're opening up to conflicts in the repo control - the errors could very well indicate such conflict, the file renaming would simply mask it but I guess changeset loss or even serious corruptions may happen especially if different machines use different versions of git
• you're losing the identity of the author in the repo history

I'd suggest creating a group-shared bare git repo (specifically designed for sharing) on that very same partition, accessible to the developer machines in the same way as the current repo (plenty of info out there, you could start at https://stackoverflow.com/questions/7632454/how-do-you-use-git-bare-init-repository):

• developers would git clone/git pull from this bare repo into their own local working repos where they make git commit their changes and then git push them back into the shared repo
• another repo would be pulled by www-data from the bare repo on the linux server for serving the development websites; a git pull in this one would 'refresh' the content with all commits pushed in the bare repo since the last git pull (a httpd restart may be needed as well after that)