The International Federation of Actors (FIA) which brings together those working on international projects has a good track record of fighting for decent rights of workers employed by the entertainment industry in those nations with poor industrial relations laws.
The union is fighting to ensure rights to cancelation payments to workers hired and then dropped from the production and a minimum wage and rights at work. In response to these reasonable demands the makers of the film have threatened to move production to a country they say will provide less rights to the workforce.
You will not be surprised to learn the statement includes phrases like bully boys, or raises the spectre of a political union, although it was interesting to read that Disney do not use Australia for films in order to avoid their strong unions there. For shame Bambi, for shame.
Less interesting is the way Jackson says he is pro-union then goes on to type a rambling screed on how much damage unions are doing to film making. As Jackson threatens to move production from New Zealand he says "if the Hobbit goes east (Eastern Europe in fact) -- look forward to a long dry big budget movie drought in this country."
The most crucial point of all though is that Peter Jackson claims it is illegal for him to enter into collective bargaining with a union. If that were right it would mean the focus of the campaign should be against the state not the production at all, and he'd have a legitimate grievance.
So I looked up what the government had to say on this. They say "Unions have a right to represent their members in relation to any matter involving the members' collective employment interests. Unions also have the right to negotiate collective agreements."