Speaking of the Constitution, if wearing the headdress is a religious thing, then what about the freedom of religion of the female cadets. This is different than respecting another country's culture in their country, and not going out of your way to antagonize them.
But I'm antagonized by the site of those female cadets putting on that religous head gear that demeans women. They are not just women, they members of the US Armed Forces, and future commissioned officers.
It is customary in Catholic Masses for women to cover their hair. Non-Catholics visiting a Catholic Church who are aware of this normally comply, out of respect.