Because they are activities that the military has no place taking part in, ever. The role of the military is to kill people and break things. Their sole purpose is supposed to be to repel foreign attacks. The founders warned us against a standing army. If modern warfare compels us to have one anyway, we must have a strict prohibition against law enforcement by military. I would even go so far as to amend the Constitution to prohibit their use.
Chasing down moonshiners, enforcing hate crimes, and strike busting have nothing to do with national defense and everything to do with martial law.
If the Yankee Army had stuck around for a few more decades, then perhaps blacks in large areas of the south wouldn't have had to wait until the 1960's to be able to vote.
You may not have noticed, but in most countries the army interferes with free elections. This typically results in civil war. Take Zimbabwe for example. Involving the military in domestic elections is a huge risk. If the wrong people are ever in power, tyranny results.
As for the KKK, what do you have against arresting those who terrorized and murdered innocent people?
I have nothing against them being arrested. I have a HUGE problem with the military arresting them. That is a job for civilian police.
As a serious student of history, yes, I occasionally have taken notice of such trends. However, we are not most countries and never have been. You lose credibility when you equate Mugabe's henchmen with Union soldiers.