I don't think we're fundamentally in disagreement, but I object the notion that people raised in Western countries wouldn't behave like the "clients" in the article do. "Culture" isn't as simple as that -- social norms differ widely within Western cultures and even at the regional or family level. Based on older stories about human trafficking, a lot of "patrons" hail from countries we would consider better than that, and many of them are middle-class or even upper-class, so it's not just a matter of social status either.
Yes, it's difficult to change someone's behaviour by talking at them. The only reliable long-term change in behaviour can be brought about during childhood. Just consider religion: sure, there are adult converts, but a fraction of adults converts from the religion they were raised in to another. A person's religion (and religiosity) is mostly an artefact of how and where they grew up.
> Human trafficking and slavery are wrong because they are wrong, because they are evil.
Evil is an intuitive but ultimately ineffective concept. These behaviours are harmful both to the individual and to society at large. They unilaterally violate the personal liberty and human rights of the victim. That's why we consider them evil, not the other way around.
I'm defining natural in terms of animal behaviour because it's the closest we can get in order to draw conclusions about how humans would behave in the absence of ethics and a functioning society. Rape and murder in cold blood are what we see in extreme situations where society has effectively collapsed (e.g. during war, starvation or epidemics).
There's a reason we say people act like animals in these situations: it's because they do. Starvation, anxiety, duress, etc, they all impact a person's capability of rational thought and lead to people following their most basic instincts. Many people still act "human" in these situations, but in general, you're going to see far more horrific behaviour than otherwise (especially if "one thing leads to another", e.g. because of group dynamics).
Also, if we understand that slavery is wrong not just because it is evil, but because it is demonstrably incompatible with a notion of right and wrong based on minimizing human suffering while maximum personal liberty, it is obvious why it is objectionable to tolerate cultures that consider this behaviour acceptable.
In other words, aside from the ethically neutral aspects of a culture (e.g. creation myths, funny hats and silly rituals), one culture can be objectively better or worse than another.
Of course changing worse cultures for the better is a long and time-consuming process. The recent failures in the Middle East and the Arab world are good examples of why you can't just invade a place and force the inhabitants to adopt modern values.
But teaching someone to be a good person is much easier when they're well-fed and don't have to fear for their life, health or fortune.
(For the record, this isn't about Islam or Christianity or even any religion at all -- any culture that perpetuates harmful values has to change, whether those values are based on religion, tradition or mere lack of consideration; religions just tend to get more offended when you try to tell them they are wrong.)