‘What’s a patriot?’ Americans stumble over dueling definitions.

Leaning against a fence near the stoop of the Georgia State Capitol, a man who goes by Nadir Xena and his friend Shadow call up to National Guardsmen standing above. “How’s your day going?”

Some of the troops chuckle.

Mr. Xena is in fatigues and combat boots. His partner wears a red bandanna as a mask; a streak of purple runs through his hair. Both are white. Like many gathered at the statehouse on Sunday, both had long rifles slung over their shoulders. But unlike the National Guard...