It seems like Parallels Tools for Linux are not permitting exec bit in umask when creating files. Manually setting the permission (chmod +x ./file) works, but no creation of executable files is allowed. I have tried to remount the shared folder with explicitly set "exec" option - didn't help.
I have this problem, too. Don't expect an answer from parallels in this forum. They don't talk with their customers. And dont expect soon a fix, it took years that they fixed symbolic links on shared folders... It's realy s shame for developers that the creation of executable files on shared folders are not working. I think i will evaluate VMware Fusion, they seem to have a better Linux support as Parallels