Soldiers are not trained in police procedures or law. When deployed in a military operation, they do not obtain or even think about warrants.
It is the responsibility of the national command to not deploy soldiers in a police operation. The military is therefore not exempt from the Fourth Amendment, but it is a matter of Monday morning quarterbacking. If a judge finds months later that the circumstances were not a proper military operation and a warrant was required, then the person whose rights were violated has a cause of action against the US.
In that sense, you have to reverse the logic. It is not that warrants are not required for a military operation, but rather than when warrants are required, it is not a legitimate military operation and should have been conducted by the police.
The most likely scenario in the current conflict is not Gettysburg, but Mumbai. A commando raid by an enemy unit arriving in fast rubber boats launched from a ship off the East Coast. Although local police might respond, it would be legitimate to also use military forces. Once committed to such a battle, soldiers can enter any building, detain people, and use such force as is necessary to accomplish the mission. If they happen to stumble into your basement filled with pot plants, that is probably not admissible as evidence in any criminal case.
Now you may say there are exigent circumstances. That provides a rationale in current legal terms for the activity. However, you are trying to apply legal language to a situation where that law does not apply. The military, once legitimately deployed in defense of the US against an external invader, do not require warrants ever, their actions are inherently reasonable, and the Fourth Amendment is silent about such activity. In the history of the US, no military unit has ever obtained a warrant for anything. A warrant is authority from the Article III branch of government to do something. The Article III branch has no authority that is required or even helpful to military operations, which operate solely under Article II authority.
There is no case law because previous generations have understood this principle. Since the Civil War, one might look for incidents in the New Mexico raids by Poncho Villa, or the martial law in Hawaii after Pearl Harbor. However, there are not a lot of examples of actual attacks by a foreign force inside the US, so you have to use some logic to guess the outcome when an issue has never been litigated.
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