Muslim Soldiers and the Constitution

My friend Seth Lipsky, author of the new book, The Citizen's Constitution: An Annotated Guide, tells me that Bryan Fischer and other extremists who want to ban Muslims from service in the American military don't have a constitutional leg to stand on:

The most emphatic single sentence in the entire constitution of the United States is in Article VI:
"  . . . no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States . . ."
The plain language couldn't be more emphatic: " ... no  ... ever ... any ... " One could argue about whether a military post is an "office" or a "public Trust" but my guess is that it easily fits the bill (notary public was the big Supreme Court case on the matter).