When I write that “voluntary mutual aid societies and workers\’ unions” are among the “myriad other ways for free people to choose individually to cooperate without cash exchanges,” I do in fact mean for the word “voluntary” to mean something. I agree with you that government labor bureaucracy, and government agencies (such as the National Labor Relations Board in the U.S.) that force employers to bargain with unions based on a majority vote of the workers, are violations of the rights of employers to chose who or who not to bargain with. But that’s no more an indictment of unions per se than the existence of government-supported monopoly corporations or government-created captive markets for large corporations (such as government-protected electrical, gas, water, local cable, or telecom monopolists; or such as the government’s use of force to, e.g., force unwilling customers to buy auto insurance) is an indictment of corporations per se.
Labor unions, as a form of voluntary association, existed and flourished in the United States (to take one example) for about 65 years before the Wagner Act was passed, and during that time they did their work without government patronage, and, indeed, often in the face of government persecution and tremendous amounts of violence, directed against even nonviolent strikers. Today, there exist successful fighting unions that do not participate in the NLRB system, either because they object to the bureaucratic process (as with the Industrial Workers of the World), or because the workers they represent are legally excluded from NLRB recognition (as with farmworkers’ unions such as the UFW, FLOC, and the Coalition of Immokalee Workers). In fact, in an age of plummeting union membership and constant schism among establishment unions like the AFL-CIO or “Change to Win” (ha, ha), these non-recognized unions are among the only unions that can report any real success in recent organizing drives. I conclude, therefore, that labor unions can and do exist without “government sanctions of monopoly and compulsion.” You admit as much at the end of your comment; but given that it is true, it’s curious that you’d object to including them on the list of forms of voluntary association that free people might choose to engage in. Do you also object to saying that free people might set up private schools, since after all schooling is mostly carried on these days by government and at taxpayer expense?
That said, while I agree, again, that the NLRB and its regulations are instances of coercion, I can’t agree with your claims about union shop or agency shop contracts. (That is, contracts in which a union and an employer agree that new employees must become a member of the union, or must pay in a fee as a substitute for their dues if they choose not to become a member.) There is in fact absolutely nothing in free-market theory which would forbid an employer from making such a contract as part of a bargain with a labor union; in a free market, employers and workers can make any kind of contracts about hiring and firing that they want to make. The fact that unions have an artificially strong bargaining position due to NLRB coercion is, of course, a violation of the rights of the employer; but adopting a particular kind of restrictive hiring agreement as a result of that bargaining, even in the existing unfree market, is not a violation of the rights of non-union workers. Prospective workers do not have a right to override private contracts in order to secure some particular job, and bosses have no moral obligation to give jobs to workers who won’t join the union, if they have have agreed to sign on to a more restrictive set of hiring practices.
Nor can I agree with your claim that a strike is an “example of union coercion.” This is absurd; all workers have a right to quit working, either individually or en masse; thus they have a right to go on strike. And if workers decide to join a private association, like a labor union, which has private disciplinary procedures for members, then that association has every right to hold them to their agreement. If you don’t like it, you should quit the union. If you can’t quit the union without quitting your job, you should quit your job. Losing a job is sad, but it’s not a violation of your rights. The world doesn’t owe you a living and if, in order to get a job you wanted, you agreed to sign on to a contract stipulating that you’d join the union and abide by union decisions to strike, then you can hardly complain that you’re being “coerced” just by being held to the terms of your contract. Nor can I agree with the claim that a union picket line is, just as such, a threat of violence against those who would choose to cross it. Of course, there have been cases in the past where people who nonviolently crossed picket lines were subjected to vigilante violence against their persons or against their property. That sort of thing is wrong, dead wrong, and should be condemned as invasions of the freedom of those who would chose to cross them. But there is nothing about a picket per se that demands or threatens that kind of bad behavior: there are lots of perfectly peaceful picket lines, and I can’t for the life of me see why the violence of some picketers should be used to impugn other picketers who never threatened anything of the sort, or who conscientiously swore off any kind of violence whatever. Certainly the form of unionism I have in mind, when mentioning labor unions as one potential form of voluntary cooperation, is the form of unionism that FW Joe Ettor proposed, when he said, during the great Lawrence textile strike of 1912:
“If the workers of the world want to win, all they have to do is recognize their own solidarity. They have nothing to do but fold their arms and the world will stop. The workers are more powerful with their hands in their pockets than all the property of the capitalists. As long as the workers keep their hands in their pockets, the capitalists cannot put theirs there. With passive resistance, with the workers absolutely refusing to move, lying absolutely silent, they are more powerful than all the weapons and instruments that the other side has for attack.”
Finally, I think it is a mistake to claim, as you do, that government labor laws unilaterally put a “heavy thumb … on the unions’ side of the scale.” It’s true that government labor laws grant substantial privileges to a certain kind of labor union (the kind that wants and can get NLRB recognition). But it also imposes substantial regulatory burdens; the government patronage comes with government strings attached. For example, it is completely illegal for NLRB-recognized unions to engage in wildcat strikes, secondary strikes, or secondary boycotts; they are absolutely forbidden from holding out for closed shop contracts and, in “Right to Work” states, are legally forbidden from even getting a union shop contract; union hiring halls are illegal; declared strikes can be, and have been, declared illegal by the arbitrary fiat of the President of the United States. All this means that some unions are privileged by the NLRB system — generally, relatively conservative business unions, like those in the AFL-CIO and “Change to Win,” who operate mainly through collective bargaining processes with management, who limit their tactics to backroom negotiations and limited strikes, who limit their goals to job security clauses or benefit packages in a conventional labor contract, and which retain a team of professional labor lawyers, union bosses, and full-time “organizers” to do their work. Meanwhile it burdens or outright criminalizes other kinds of unions, which used to be much more prominent in the pre-Wagner era — rank-and-file-run unions like the I.W.W., who generally refused collective bargaining, favored minority unionism, direct action on the shop floor, solidarity strikes, general strikes, union hiring halls, and other forms of action that didn’t depend on maintaining any kind of bureaucratic interface with the boss or the State.
For more on wildcat unionism and free market principles, see my articles “Free the Unions (and all political prisoners)!”  and “In reply to a reply by Walter Block and J.H. Huebert” , my series of articles on the Coalition of Immokalee Workers and the series of victories it has won through government-free wildcat unionism , and Kevin Carson’s essay “The Ethics of Labor Struggle: A Free Market Perspective” .
Hope this helps.