Nugent behaving like an idiot only hurts those he supports. A Democratic plant would be an equivalent.
The goal is to win. Nugent does not help.
Nugent, though he may be a personally loathsome creature, is a counterpoint to what the Left fronts as activists. As such, Nugent is perfectly useful and no worse a public figure for attacking the Left.
Nugent is, suffice to say, a much better advocate than the usual squishy, spineless, weak, timid pussies that the Right usually prefers as “warriors” against the Left.