Created xdg-utils tracking bugs for this issue:

Affects: fedora-all [bug 1194209]

Analysis:

xdg-open is used to open a file or URL in users preferred application. During the process of finding the correct app to run, it recursively searches Desktop file in function search_desktop_file(). This function uses local variable $file to store the path to the searched Desktop file and runs function get_key() on the $file. get_key() searched for 

[Desktop Entry]
Exec=...

in the $file and content of Exec= is later executed.

The problem is that variable name $file is also used earlier in function open_generic() and stores path to the file being opened. Now assuming that system`s shell *does not* reset the content of $file when it is declared as local variable *again*, then the file being opened will be searched as Desktop file. If it contains expected [Desktop Entry] along with Exec=, it leads to arbitrary command execution.

The assumption about reset of local variable contents hold for dash, but not bash:
$ cat testme
testme() {
   x=backfromthedead
   local x
   echo $x
}
testme

$ dash testme 
backfromthedead

$ bash testme 

Also, this does not work if the local variable is initialized:

$ cat testme 
testme() {
   x=backfromthedead
   local x=""
   echo $x
}
testme

$ dash testme 

$ bash testme 

xdg-open as shipped in Fedora and RHEL-7 does initialize $file variable, and uses bash as default /bin/sh.

Statement:

This issue did not affect the versions of xdg-utils as shipped with Red Hat Enterprise Linux 6 and 7.