Given that unions are covered under the right of free association, it should be obvious that libertarians are not anti-union. It is well known among opponents of libertarians that libertarianism supports free association, to the point where the fallacious argument is made that arguments in favor of free association are actually a cover, in the form of eloquent verbiage, for racism.
Yet for some reason a philosophy whose greatest pride is its consistency is expected to abrogate the right of free association if the association is called a union.
Unlike the traffic light argument there may be a somewhat reasonable source for the union argument. Given the current state of affairs, where the government is a club to be used against ones opponents, not wishing for one side to have the club is considered by default to want the other side to have the club.
A hypothetical scene from the Lord of the Rings may best describe it, the characters being familiar enough so that twisting them into slightly new roles is possible.
Sauron (representing big business) and Saruman (representing unions) are both trying to convince Frodo (representing libertarians) to hand over the Ring of Power (representing power).
Saruman: Frodo, you must give me the ring, otherwise Sauron will have it. I only have your best interests at heart.
Frodo: But I want to destroy the ring.
Saruman: No, since you don’t want to give it to me, it is proof that you actually want to give it to Sauron.
Frodo: What? No, I want to destroy it because I don’t want anyone to have it.
Saruman: No, that’s just fancy words you are using to cover up your true desires. I’m tired of your hobbit double talk. You really support Sauron. Look, by walking to the Cracks of Doom, you are walking to Mordor, which shows you want to give him the ring.
Given that many are incapable of imagining one actively not wanting either side to have power, and the Manichean outlook produced by the two party system, a person can be forgiven for initially thinking that since libertarians don't support special government favors for unions that they must support special government favors for businesses, but only until they actually meet their first libertarian.