This fury may be because data is hard to get on some aspects of prostitution, such as the demand side (the "johns") and also because data about trafficking and exploitation is, almost by definition, also difficult to obtain or interpret. That leaves the debate wide open to individual views. Those, in turn, depend on the individuals and their places in the hierarchies of the sex work marketplace. Questions of "choice" and "agency" and such abound, but it's hard to get solid numerical data on the characteristics of mostly illegal markets.
So the debate is all over the place. On one extreme endpoint, sex workers are seen as women (mostly women) who were abused as children and never had a chance, who were possibly trafficked as sex-slaves or trapped as teenagers in the streets, who are addicted to illegal drugs, who are exploited by pimps and who are essentially powerless to stop any of it.
The other extreme endpoint argues that there's nothing more exploitative about sex work than about, say, washing the bottoms of the elderly in a nursing home, that sex work is no different from any other poorly paid and exploitative occupation, such as flipping burgers, washing floors or serving customers at a Hooters bar. According to this view, choosing sex work is a rational choice, especially for those whose other options are all linked to basic survival, and choosing sex work in the higher-paid part of the market is also a rational choice, because of the pay and the freedom the work offers.
Given those extreme viewpoints (and others), it's obvious that political responses to how sex work should be arranged, whether it should be banned or legalized, whether it should be taxed and regulated etc. have a similar spread, though most real-world opinions probably fall somewhere along the line connecting those terminal points.
Pollitt argues that the political left seems to be changing its take in these debates:
On the left, prostitution used to be seen as a bad thing: part of the general degradation of the working class, and the subjugation of women, under capitalism. Women who sold sex were victims, forced by circumstances into a painful and humiliating way of life, and socialism would liberate them. Now, selling sex is sex work—just another service job, with good points and bad—and if you suggest that the women who perform it are anything less than free agents, perhaps even “empowered” if they make enough money, you’re just a prude. Today’s villain is not the pimp or the john—it’s second-wave feminists, with their primitive men-are-the-enemy worldview, and “rescuers” like Nicholas Kristof, who presume to know what’s best for women.Is the US political left changing its views? This is another aspect of the debates on which we have very little statistical data. I recall those attitudes existing in the past, too, for what that is worth.
What's odd about the feminist chunk of these debates is how all sides use feminist arguments for their opinions, though picked from different types of feminist theories or schools of thought.
I can begin by reading about oppression, exploitation and horrific violence, all aimed at sex workers by their customers or by their pimps, then move on to read about the problems with the feminist savior industry, the need to regard those who engage in sex work as having chosen it as empowered free agents and the need to simply leave the market alone or to legalize it, then move to reading upsetting stories from trafficking victims, and then finish the day with two articles, both stating that the voices we need to privilege are the voices of the affected women alone, except that the affected women in these stories have opposite beliefs about the correct remedies.
None of the above is intended to belittle any part of the ongoing debates, nor intended as an exhaustive summary of what's going on in them. What I wish to highlight, however, are a few deeper layers in how the markets for prostitution differ from most other labor markets, because these layers tend to fall by the wayside within the activist circles.
First, if we regard the markets as sex work from an economic point of view, then almost all the debate focuses on the supply side of the markets: Those who sell sexual services in exchange for money (the sex workers) and those who manage the sale of sex in exchange for money (the pimps).
But the markets also have a demand side: Those who buy sexual services with money. Though the debate is not silent about the johns (see Pollitt on that), the treatment of prostitution certainly privileges the study of the supply side in that many of the pieces I have read simply take the demand side for granted, as something which has always existed and always will exist, as a natural force, and then hastily resume the study of the problems on the supply side. But there would be no market without demand.
Second, being a sex worker does differ from many other jobs, whether poorly paid or not. For one thing, it's vastly more dangerous. This could be mostly because prostitution is usually an illegal occupation, but it could also be the case that some fraction of the clientele of sex workers are, in fact, "buying" the "right" to act out violent feelings.
Third, and here we move into even deeper layers: When someone is angry at another person on a political site or elsewhere on the net, that person doesn't call the focus of his (or her) anger "a nursing home aide" or "a coffee bar server" but "a whore". Indeed, the occupation of sex work is the most stigmatized occupation of any I can think of, and those who use terms such as "whore" as slurs are quite likely to be men (though women use those slurs, too).
I don't think we can simply argue that prostitution is no different from many other poorly-paid female-dominated occupations, given the tremendous load of negative feelings which are attached to it. There is something different about sex work on that level. If I had to make one single guess* about the reason for the stigmatization of sex work, it is that those who might imagine themselves to be its customers** regard the idea of someone selling sex, rather than giving it because of love and admiration towards the potential sexual partner, as insulting or hurtful or disgusting. The alternative script for sexual interactions is, after all, based on love or at least on mutual sexual attraction. To have to pay for sex then looks like a rejection, of sorts.
Fourth, and finally, and on the deepest levels of all, the markets of sex work are gendered in ways which few other markets are. The sellers are predominantly women, the buyers are almost completely men***, and the gender of the sellers matters to the buyers. We couldn't switch the gender of, say, half the sex workers, the way we could switch the gender of many other low-paid workers without fundamentally changing the products of the market. That most of the sellers are women is an essential aspect of the product in sex markets, for the heterosexual men who dominate the demand-side.
Why this is the case can be debated, from biological arguments about men "needing" sex more than women (though see this article on some different historical ideas) to the arguments which look at the actual history of sex work.
Those point out that women didn't have access to money with which to pay for outside sex, that women often didn't have access to "outside," and that the punishment for extramarital sex was always disproportionately larger for women than it was for men (whether the women were regarded as prostitutes or just as "loose" women). Thus, sex markets for women couldn't really have been created, even if men and women had equal libidos, and even if the gendered problems of unwanted pregnancies and potential violence from bigger-and-stronger strangers had been solved.
Whatever the reason for that gendered essential nature of the sex work markets, at least today***, we should not erase it in our arguments about sex work as a labor issue or as a safety issue, because it does matter for full understanding of the field.
*Though a more complicated explanation is probably the correct one, including some generalized misogyny and sexual entitlement ideas. But I do think there's an element of anger based on hurt in this kind of thinking.
**A single guess is hard to hold on to here, because it's also true that once the meme of a whore is out there, everyone understands that being called one is not a compliment, even without thinking through the reasons for it, and the word gains more and more power as an insult.
***With certain exceptions, as discussed in this article and this one. That those stories describe a power imbalance based on income and race may also play a role in sex markets of the more traditional type where the buyers usually are better off than the sellers.