Actually, quite the opposite - in a free market, labor is free to organize in any way they want. If they have enough leverage over the employer, they'll succeed.
The anti-free market part is the regulatory quagmire that the US has in place for organized labor.
I think that's the thing that most people take umbrage with.
I don't know for sure, but I've heard from knowledgeable folks that it is more effective in Europe.