One reason is that it would be political suicide for the GOP.
IMHO, the folks who make these kind of suggestions are, most of them, good people, but what they are saying tends to discredit FR and conservatives generally.
The Israeli Defense Forces have, as a percentage, way more Muslim soldiers than does the US. And I have never heard of an Arab-Israeli soldier killing Jewish ones. What this tells me is that we need to better screen incoming soldiers to make sure they are patriotic, not to set up a religious litmus test.