Careful: chmod -X also looks for any existing exec bits:

$ umask 0
$ >foo >bar
$ ls -al foo bar
-rw-rw-rw- 1 user group 0 Sep 10 00:00 bar
-rw-rw-rw- 1 user group 0 Sep 10 00:00 foo
$ chmod o+x foo
$ ls -al foo bar
-rw-rw-rw- 1 user group 0 Sep 10 00:00 bar
-rw-rw-rwx 1 user group 0 Sep 10 00:00 foo
$ chmod u=rwX,g=rX,o=rX foo bar
$ ls -al foo bar
-rw-r--r-- 1 user group 0 Sep 10 00:00 bar
-rwxr-xr-x 1 user group 0 Sep 10 00:00 foo