MSYS is not the problem. Even if MSYS chmod doesn’t work (it doesn’t), Git has a built in way of getting around that problem, i.e. git update-index --chmod=+x. Let it be clear that git update-index only messes with the index (staging area), not the local repository (working directory).
I am convinced the problem is with GitHub. On GitHub if a file is initially pushed with mode 100775, all is well. If a file is initially pushed as 100644 it causes a problem. Attempts to change the file mode will succeed with git add, succeed with git commit, succeed with git push, and even show up in the GitHub file history, but not be reflected on the “blob/master” page on GitHub.
Update
From: Petros Amiridis (GitHub Staff)
Subject: How to change FIle Mode on GitHub?
I have some good news. Our awesome team has just confirmed it is a caching bug
on our end. Our team has deployed a fix.