Как удалить только режим файла из индекса GIT

Этого можно добиться частично, установив для параметра core.fileModeзначение false :

git config core.fileMode false

Это приведет к игнорированию исполняемого бита (и только этого бита ).

Цитирование документации git-config:

Tells Git if the executable bit of files in the working tree is to be honored.

Some filesystems lose the executable bit when a file that is marked as executable is checked out, or checks out a non-executable file with executable bit on. git-clone(1) or git-init(1) probe the filesystem to see if it handles the executable bit correctly and this variable is automatically set as necessary.

A repository, however, may be on a filesystem that handles the filemode correctly, and this variable is set to true when created, but later may be made accessible from another environment that loses the filemode (e.g. exporting ext4 via CIFS mount, visiting a Cygwin created repository with Git for Windows or Eclipse). In such a case it may be necessary to set this variable to false. See git-update-index(1).

The default is true (when core.filemode is not specified in the config file).

Хорошая ли это идея — другой спор...