Real question is: "Why do we salute?"
Saluting is the RSM's version of "touching the forelock".
Touching the forelock is what men did to show respect to superiors when they didn't have a hat to remove.
Removing/Tipping the hat was common when meeting someone in the street.
And even in my day, when wearing caps to school was common, the "gentlemanly" thing was to tip your cap on meeting people, take your cap off as soon as you entered a house, and nobody ever sat down to table wearing any kind of hat - that would get your ears boxed.
There is no religious significance at all.
By the way, Sikh boys at the schools I attended always kept their topknot covered, both in class and on the sportsfield.