Civil rights movement if KKK specifically targeted black servicemen in Deep South

http://en.wikipedia.org/wiki/Lemuel_Penn

Lt Col Penn was probably the most prominent serving black army officers murdered during 1960s civil rights-era violence by the KKK in the Deep South. Now, WI such violent attacks against black servicemen in uniform were more widespread & systematically conducted by local white supremacists (whether local sheriffs or their cousins) in that timeframe- perhaps to the extent of undermining unit strength & cohesion at places like Ft Benning or Ft Bragg ? Would the (integrated) US armed forces, with federal govt support from other agencies as necessary, take effective action to hunt down the perpetrators of such racist violence, were there substantial nos. of their own men being so targeted & restricting combat effectiveness ?
 
This is a gruesome POD.

I imagine the public outcry would be greater vs the Klan long before it'd affect unit cohesion.

And you can't send in the troops to go after the Klan. It's not comparable to public disorder like in the Little Rock school desegregation riots. They might send in military investigators, but that's it.
 
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