Great question Special-K.
I suspect the looking for extremists will only be in the officer ranks. Enlisted men are generally left out of this kind of politics.
There are several quiet ways of dealing with officers other than dishonorable discharge. Actually, an officer can not be reduced in rank or DD'd unless handed down by a general court marshal for crimes like, treason, espionage, desertion, sexual assault, murder, etc.
The ways these officers can be taken out are by three consecutive poor reviews, ask them to resign, or a reduction in force like after a war. We don't need you anymore brother. But, in all sincerity, who knows in todays military.