No, religious beliefs are no way to measure patriotism. Historically, men of all faiths have fought and died alongside one another in modern American conflicts, from the world wars to Iraq and Afghanistan. Having served in the Army myself, I can confidently say that one and only concern is to protect and assist the brother in arms next to you when the bullets start flying. Regardless of race, gender or faith.
I don't think that a person's religion has anything at all to do with their level of patriotism or their ability to do their job. The only exception to this would be those who are extremists in any religion. You can be a patriotic American and a good soldier whether you are Christian, Muslim, or even an athiest.
The other soldiers serving with Humayun Kahn did not realize he was Muslim because religious faith and practice is a very personal matter for true believers and most people of faith. They do not need to force their personal beliefs on others. Whether religious or non-religious, it is possible for people to love their country equally.
Yes, religion is not an adequate measure of a soldier's personal level of patriotism. One can a member of the Muslim, Catholic, or Protestant religion, or of no religion at all, and still consider themselves, and be considered as, highly patriotic. Although religion can influence patriotism, it is not necessarily a determining, or limiting factor.