SELinux messes things up badly. disable it as there is little to none upstream support of specific selinux configuration. Most assume that if You have selinux, you know how to deal with it Yourself.

Apparently, apache web server use different user (called "apache") when running its process.
Giving write permission to the repo directory for this user solves the problem.

I had the same problem, and its always a mess to find the solution. It appears if you do not follow all the instructions on how to set up the git repo to the letter and take a shortcut by running the deamons as root. If you run into this ( on a debian mashing that runs apache as the user www-data ) you have to make sure

1. That the deamons are running as www-data. ( or prob evem better follow the instructions on how to run them propperly )
2. Make sure /var/repo exists and the www-data has read and write permissions to that folder.

Usually if you create the repo with a deamon running as root www-data will not be able to push to that repo.