To put this into other words, a "right to work" is a positive right. It implies an obligation of someone else to hire the person in question. Similarly, a "right" to food, clothing or shelter would oblige others to provide these things for the persons who have such "rights." But positive rights are a direct violation of the libertarian code, which is based upon the non aggression principle. These types of "rights" are a not so subtly hidden demand for wealth at other’s expense, e.g., they amount to a call for, or support of, theft. No libertarian can support them.
In contrast, libertarians do indeed support negative rights, the right not to be murdered, raped, aggressed against. And, yes, this does impose an obligation upon others – to refrain from such nefarious deeds.
Forbidding political participation, compelling democracy, imposing right to work laws, etc., are all second best attempts to wrestle evil unionism to the ground. If it is politically possible to counter organized labor in any other way, these sorts of things may well be justified. But, if we are to properly apply libertarian principles to this arena, let us have no more of this "right to work" nonsense. We should leave off actually believing that voluntary agreements for union or closed shops for some strange reason are compulsory. Of course, they are not. They are merely an instance of monogamy in labor relations.
If we are to effectively promote libertarianism, we must start off by accurately understanding our own philosophy. Proponents of "right" to work legislation fail in this regard. At the very least, if they fully understood libertarianism, they would say something like: Of course, there is no "right" to work. However, rampant unionism is running amok, and the only way we can deal with this menace to civilization is via right to work legislation (or prohibiting them from engaging in the political process, or shoving democracy down their throats, etc.) We favor right to work laws not because they are just, per se, but due to the fact that they ward off a far greater evil.
.. There are problems with it. It is all too similar for my tastes to Milton Friedman's proposals for school vouchers, etc. But, at least people who argue in this way demonstrate a keen appreciation of what libertarianism is all about. There would be something to be said in behalf of these laws on that ground alone.