Some things to point out:
In a Conservative state like Indiana, yes, Conservatives are often fiercely intolerant of anything they perceive as anti-Christian or against what they believe to be American values. You can expect to encounter at least a few that will openly display hostility towards an Atheist. Former governor Mike Pence passed a law that allows religious people to discriminate against LBGT people, and he bitterly fought against having the state issue marriage licenses for same-sex couples. Even if you support the military but also support a budget cut for them and reduced wasteful spending, be ready to clarify a hundred times you don't hate the military and aren't opposed to them, just opposed to having them in bases where we haven't had in fighting for generations now.
One of the ways Conservatives are violent is their passage of laws that are detrimental to women, immigrants, LBGT, black people, and various other minorities. They will work to make their lives difficult, hard, and reduce their quality of life as much as they possibly can until the Supreme Court steps in and says no more (this happened more than once with Pence).
Attacking the innocent is always wrong. But, in instances like Virginia, the protesters do actively and explicitly call for violence against others (and, indeed, a counter protester was killed). A counter protest to this should not be condemned, nor should we tolerate speech that actively and explicitly promotes/condones violence. These aren't Tea Parties waving signs about keeping government hands out of medicare, crude racist statements, and grammar/spelling errors here-and-there, these are people who actively support violence and discrimination against various groups, and often enough act out on those views. We don't have to or need to ban Nazi flags, and we also do not need to tolerate them, we don't want to tolerate them, and we shouldn't be crying foul against counter protesters who stand up to such hatred.