From the Right
Many people come from a religious background whose teachings say that certain types of sex (which overlap heavily with sex work) are inherently morally wrong. This could be: sex outside of marriage, sex before marriage, sex for recreation instead of procreation, non-straight sex, etc. Regardless of whether someone remains a member of the church they were raised in, they may still strongly agree that these types of sex are inherently bad, period.
People are perfectly entitled to feel that way, and I’ll just have to agree to disagree with them on that point. It bums me out a bit, because I think they’re missing out on some nice stuff — but they think that I’m missing out on eternity in Heaven, which must be a bummer on their end. Fair enough.
So I would never take issue with someone’s belief that sex work is inherently immoral. The problem is what to do about that belief. Just as most of the country has come around to the idea that gay people should be able to have families and live their lives, even though some people find it immoral, then just because some people find sex work immoral doesn’t automatically mean that it should be legally forbidden.
And that’s the key: the fact that some people believe something is immoral is not enough of a justification for why it should be made illegal for everyone. There is a higher burden — such as demonstrating gross harm to society. Accordingly, a more moderate conservative may concede the point on gay marriage, but argue that, unlike the relatively small ‘harm’ of gay families, sex work is much more pernicious and therefore needs to be handled differently. More on that here. But just saying “I think it’s immoral” isn’t justification enough for why banning it is the best course of action.
From the Left
This probably isn’t news to anybody, but: feminists are not a monolith. By far the strongest support for and pushback against sex work I’ve ever encountered has been from people who all strongly identify as far-left feminists.
Some of their biggest concerns about sex work that I’ve seen are as follows:
It promotes the objectification of / violence toward women
It reinforces unrealistic beauty standards
It’s synonymous with human trafficking
It’s extremely dangerous for trans folks + people of color
It teaches people to have sex badly (probably not as dire a problem, but one of my personal worries)
These are all fair concerns. But I’d argue that sex work, with proper regulation and oversight (as we do with any industry), can easily do more good than harm — and that these concerns from the Left are better resolved by legitimizing sex work than by banning it. More on that here.