The meaningful division is between those who use coercive manipulation of the bounds within which economic activities take place, and those who rely on voluntary, cooperative courses of action. Any number of organizational structures, including unions, would occupy a free market, negotiating for their members, systematizing production and administering business affairs. If public workers’ unions draw special ire due to the fact that their members “feed from the taxpayers,” then we would do well to remember that their members are the taxpayers.
Members of these unions work for the formal state, as against technically (very technically indeed) private firms, but many among the latter category benefit no less from the industry of the taxpayer than do state tentacles like government schools. Libertarians in good standing are apparently meant to take a “plumb-line” approach to the unions at hand, regarding the public workers themselves as culpable insofar as they’re participants through “working for the state.” But by a standard that demonizes all of those who labor to benefit the state and those who circle around it, we are all blameworthy.