An excellent post on Vox Nova (by Katerina Ivanova on the difficulty in finding clothing that is made sustainably) contains an interesting thread of comments by people debating the repercussions of fighting sweatshop labor.
For the record, I don't agree with arguments like "But if they close the sweatshops all those people will be out of work and forced to turn to prostitution or starve!" From a wider perspective (a Catholic perspective) both slave/sweatshop labor and prostitution are equally evil and unjust. But opposing sweatshop labor is a step towards moral good: an economic society which pays its employees a fair wage. Doing nothing, or allowing sweatshops to continue as the "lesser of two evils," only perpetuates the status quo.
Each of us as individuals are morally obligated to do what we can and taking concrete, life-changing action. Yes, companies will close their sweatshops if they are told they can no longer operate them. And then what will the company do? Will they simply stop making clothes? Maybe. Or maybe they will open an sustainable, ethical shop somewhere else. Eventually (as is ALREADY happening) companies will realize the eyes of the world are on them. Companies CAN make clothing without sweatshops, so it's false to claim that denying them the opportunity to use sweatshops will destroy the industry. If all manufacturers are unable to operate while exploiting their workers, they will be forced to employ fair labor practices.
Take the United States as an example. We had child labor, slave labor, unsafe working conditions, hazardous factories dumping deadly chemicals into waterways...you name it, we've done it (and in some cases still are.) But overall, companies who operate in America comply with fair labor practices because the public and the government demands it. This has been the progression of the fair labor movement; it is the ultimate goal -- not to force one company or one country to operate effectively, but to create a society where exploitative labor is unacceptable. The most important step towards that is awareness. Without transparency, companies can flout public mores with impunity. This is partly why I consider the media (and journalism in particular) the most powerful tool for change.
The second step rests with us, the public. We must demand that companies find ways to operate ethically. It is a tragedy that this will result in the temporary worsening of many people's living conditions. The only way to mitigate such damage is to Take the Poor With You. Boycott unethical companies by refusing to buy their products. Go to that wedding in an old dress. And with the money you would have spent, contribute to charitable organizations that assist the poor and unemployed in countries affected by the boycott.
Thousands of soldiers and civilians died during World War II to rid the world of the Nazis. Pacifists might argue that since people were dying either way, the deliberate taking of another life could not be morally justified. But the Catholic principle of just war declares that it can. We must declare just war on oppression wherever we find it, even if it means engaging in what would otherwise be considered a great evil.
I believe if the greater good is being served and society is moving towards equity, justice, freedom and sustainability, then the evils that may come as part of the change are not only justified, they are in fact moral.