The rights are not necessarily waived but are subordinate to military regulations (UCMJ) in order to promote "good order and discipline". Discipline is a critical factor in the effectiveness of military units. The courts have typically trusted rulings of military courts since civilian courts are not necessarily well equipped to understand how a ruling would impact the military.
The US armed forces are not run as a democracy; it is an oligarchical tiered serfdom as near as I can peg it. When you sign up, nearly everything you agree to is in a binding legal contract with the US government, and if you breach contract, it is very different than breaching a normal contract. Part of that contract is that normal courts of law and their rules are secondary to military courts and all of their very, very power imbalanced rules.
Source: myself, a decade in the Marine Corps, witness in several Non Judicial Punishment cases, and one Courts Martial case.
here's James Mattis's take on the difference between civilian courts and military courts:
> ...remember that the Uniform Code of Military Justice is established under the U.S. Constitution, because our framers knew that those we give weapons to in this country have to be governed by a different set of regulations than the population at large.
> And under the Uniform Code of Military Justice, which was the latest in a history of these rules that came out in the late 1940s and modified often since then, the defense is actually stronger. The defendants' rights are actually stronger in a military court than in a civilian court. Just read F. Lee Bailey's book, "The Defense Never Rests." And as one of the most aggressive defense counsels in our history, he said he would rather a court--defend--defend in a military court than a civilian court in his book.
> And the reason is you have more rights in order to prevent the military court system becoming what you and I would call a "kangaroo court." So, you give the defense more rights. And when that court acts, you--for most of us in the military who have an intimate knowledge of it, we have a great deal of confidence that justice has been adhered to, in the true sense of what justice is all about toward a person accused of a crime by the government.
This was a grand jury proceeding. While this was about a matter that happened while she was in the military, anyone that is granted immunity but refuses to testify could be held in contempt by the court.
Speaking in the most general sense possible, having your armed forces firmly under control is traditionally a core part of staying in power; it's also very generally true that no person making the rules is going to actively hinder their own ability to keep doing so.
That's why it's super important to keep them aware that the little people are watching and taking notes; that's literally the only trump card we all have.
