What you call [US] conservatives (i.e. the Republican party) isn't a monolithic block of thought, but a coalition. The essence of it, as far as this discussion goes is that there are two opposite poles:
- For the religious right, (Bible) morality trumps any [Von Neumann–Morgenstern-derived] utility theory arguments for free markets, or fuzzier notion(s) of liberty like Lockean natural rights. This is basically Devlin-style legal moralism, in a US setting, which has had many names over time, Moral Majority etc. It actually has a pretty long tradition in the US Evangelical movement (which has become one of the pillars of the Republican party, as the religious right):
Following the abolition of slavery, a series of social purity movements led by middle-class
evangelical Christian reformers and other social purists gained momentum in the late 19th
century. Rooted in assumptions about women’s ‘natural’ moral nature as pure, pious, and
submissive, these movements sought to use female moral influence as leverage for enacting
wide scale social change. Tackling issues that included alcohol use, the sexual double standard and male violence against women, the goal was to eradicate ‘vice’ (understood primarily as prostitution and other forms of sexual immorality), thereby bringing all of society
into conformity with the Victorian moral values prized by middle-class evangelical Protestant evangelicals (Coontz 2005; Grittner 1990; Hunt 1999; Pascoe 1990; Pivar 2002).
Fear about ‘white slavery’ was crucial to the leverage that the social purity movement
achieved in western Europe and in the U.S. ‘White slavery’ referred to white women
held against their wills, usually involving some combination of force, deceit, or drugs,
and forced into prostitution. It elicited images of crazed men preying on defenseless white women. Replacing the degraded black slave with the demoralized white woman, the
rhetoric of ‘white slavery’ drew on and updated earlier abolitionist rhetoric about chattel slavery. Yet the ‘new abolitionists’ appropriation of the earlier abolitionist rhetoric concerning chattel slavery was riddled with racist undertones. [...]
- Orthodox/pure libertarians have a maximalist (i.e. politically extremely liberal, in the classical sense of the word) view of the self as governed by property rights, which cannot be infringed unless they interfere with the rights of others. Thus, in the extreme take on this, e.g. as exemplified by Nozick, it entails the right to even sell yourself in slavery.
So, to put it in somewhat crude terms (to enhance the contrast): an "economic conservative" is against regulation of economic life, but a religious (aka social) conservative is for the regulation of morals in society, in a specific way that matches their religion. Some US conservative writers freely point out that an "economic conservative" is what others call a "classical liberal". As discussed in that link, more generally, there's some level of tension between these two conservative-labelled viewpoints [economic vs social] on some other "big government" angles, although there's also plenty of room for some common ground.
In particular, many (on both sides of the formal political party divide in the US) would reject the extreme Nozick-style view on liberty, even if they don't fully endorse a Devlin-style view on legal moralism, by allowing plurality in some but not all respects. So, this leaves room for (many) economic conservatives to agree with social conservatives on matters like prostitution.
For example, if we take Reagan as a prototypical US conservative, and who is generally seen as having successfully married free market thought (with some limits) with religious conservatism (again with some limits), Reagan said e.g. that:
“Prostitution has been listed as a nonvictim crime. Well, is anyone naive enough to believe that prostitution just depends on willing employees coming in and saying that’s the occupation they want to practice? It doesn’t.
…Talk to law enforcement people about the seamy side of how the recruiting is done, including what in an earlier day was called the white slave traffic – and you will find that the recruiting for prostitution is not one of just taking an ad in the paper and saying come be a prostitute and letting someone walk in willingly.”
Basically, the "conservative mainstream" (to the extent that that exists anymore in the US) has it that prostitution is bad because prostitution = slavery. And you can't agree to slavery as a matter of principle. Following the same line of thought, by invoking "human suffering" and "common decency", Reagan argued that pornography, which he interchangeably called obscenity, "exploits women, children, and men alike". Thus it is basically somewhat like slavery too (although he did not explicitly use the latter word in re pornography/obscenity). Basically, a way of "meeting in the middle" for the conservative US movement to reject some behaviors was equate them with slavery, or thereabout.
Some answers here have suggested that conservatives are A-OK with porn; that isn't entirely correct; a number of social/religious conservatives in the US would still like some kind of porn ban or at least more restrictions. Politico has a good (and alas also very long) historical account of such efforts in the US. It's just that for porn the slavery analogy didn't carry that much water perhaps and there was the (major) issue of porn [bans] also butting into free speech issues. To very selectively quote the most relevant bits from the Politico account:
Emboldened [by the Regan era successes], the GOP’s 1992 platform called for “a national crusade against pornography” and endorsed sweeping government intervention. [...]
However, this all fizzled out in the 1990s and Bush years.
The simplest explanation is fatigue: Having lost so many battles during the Clinton years, only to then see the hope of the Ashcroft era vanish, much of the anti-porn movement ran out of gas. “We put the issue front and center in the ’90s. Congress was engaged, we were engaged and the technology industry was engaged fighting against us,” says Hughes, the internet safety advocate. “We had a bipartisan coalition behind us, but we were losing just about every battle in the courts. And it just demoralized so many people. I think that’s when the white flag came out.”
N.B. the heyday of this anti-porn legislative effort might have been the CDA of 1996, which one could describe as an attempt to make a Comstock-style law for the internet age; portions of it were quickly deemed unconstitutional by the Supreme Court. It was replaced by much weaker prohibitions limited to public schools. The porn-relevant bits of the COPA of 1998 were likewise struck down during the Bush years. (The final SCOTUS decision on that, finding COPA too restrictive on adults, was only a 5-4 vote though. It's also an interesting case that Scalia and Thomas voted on opposites sides on this matter. I guess the [judicial] conservatives'--by which I mean textualists'--hunch that Thomas had "unsettling" views on natural rights was proven correct in this case.) So it wasn't really for the lack of wanting/trying [from the social conservatives] that porn wasn't banned or more substantially restricted.