[NSFW to be safe]

Later medieval Latin Europe has the paradoxical reputations of being both increasingly repressive, focused on social order and purity; and being wildly raunchy. Prostitution, in a sense, slips through several cracks in medieval Christianity. First, as the Church increasingly sought to exercise control over the sex (and more to the point, reproductive-inheritance) lives of its members, prostitution was also a matter of on the ground, day to day order. Jurisdiction hung uneasily between secular (civic or manorial) and canon courts. Second, theologians taught that sexual urges were simultaneously natural and sinful, a mark of the Fall of Man on both parts. They constructed marriage as the grudgingly non-sinful outlet for carnal desire--but always within many, many boundaries even then.

As Ruth Mazo Karras shows, the idea of inherently sinful sexuality paradoxically helps justify legal (but still morally wrong, because sex outside marriage) prostitution. And here we see the marks of medieval sexism. Although theologians wrote effusively on women's insatiable sexual desire, we don't read about women visiting male prostitutes. Meretrix is feminine.^1 Since women were already Eve-n more fallen and sinful and insatiable, men just found the worst of the bunch.

Indeed, women prostitutes were seen as a "necessary outlet" for men's sexual drives. Including clergy in sufficient numbers that particular career prostitutes might develop a reputation as specifically a "monkwhore" or "prestwhore." This did not trouble the Church, it seems, so much as questions of prostitutes taking johns to cemeteries (consecrated ground) and whether the Church could profit-by-proxy from prostitution through prostitutes' alms (of course).

North of the Alps, the religious and public discourse on prostitution does get darker in 14C into 16C as noted above--the burden on public order perhaps becomes too much, although several scholars have argued that concerns over prostitution/sex/reproduction among Christians, Jews and Muslims especially in Spain bled into wider European anxieties. Known prostitutes might be restricted to certain areas of a town or forced to live outside, forced to wear distinctive clothing, excommunicated, banned from Mass at certain churches. These measures appear in some places as early as the 12th century, to be clear, but ramp up later.

Note, of course, that these restrictive measures targeted the women, not the men who used them.

Nevertheless, prostitution in the later Middle Ages was entrenched in medieval society at many levels. It is, as OP notes and R.I. Moore argues, especially tied to towns and a cash economy. But the scope of medieval men had access to prostitution.

One brutally common way, of course, was military campaigns. Medieval armies traveled with a so-called "baggage train" or camp followers, including prostitutes. (Yes, even on the Crusades.) Travel in general provided opportunities for men to seek out sex for hire. We find mentions of men visiting towns on religious pilgrimage who pay for sex, for example.

But there was absolutely rural prostitution in your average peasant village as well, although probably significantly less of it than in towns. One thing to keep in mind is the "occasional" nature of medieval prostitutes. While a lot of research focuses on brothels, especially the legal ones (because hey, sources!), one thing that numerous scholars have shown is that women (even married women) might turn to prostitution temporarily to shore up weak finances. Some of them found themselves trapped in a spiral, of course. Young women working as domestic servants to increase their future dowry might well find themselves exploited as prostitutes by the head of the household, especially to guests passing through.

We can think that a lot of temporary or informal prostitution existed in villages, although larger ones might also have their established brothel. (And again travel--just pop over to the next village, or to a town.)

Coins have indeed been found in archaeological digs of medieval villages, but scholars have suggested that prostitution in villages at least had the reputation of being for trade goods as much as, or rather than, money. Thus in Canterbury Tales:

He sent her sweet wine, mead, and spiced ale

And cakes, piping hot out of the embers

And, because she was from town, he offered money

For some folk will be won for riches

Note that the passage describes an attempted seduction rather than prostitution, but where is the boundary when the sex will be a sin?

Karras does suggest that manorial (secular) courts were less concerned with prostitution than towns' secular courts, although in some situations the Church's moral jurisdiction bridged the gap.

One interesting difference between rural and urban courts, at least in England, is the higher percentage of cases in rural courts where we observe a bawd being charged but no contemporary prostitute. Bawd could be a formal pimp or procurer, but it was also the crime of arranging any illicit sexual encounter, not just for hire. Perhaps the exchange of goods instead of cash was a lesser crime, or the transaction was for social benefit--or maybe this was the manorial Tinder in a way that towns didn't have.

In general, prosecution and persecution focused on women. There were some situations where men might appear before the law. For example, in canon courts, married men might be charged with adultery for having sex with a prostitute. Or men could be charged as procurers or with running an illicit brothel. But most of the social stigma as well as legal consequences came to lay on women.

Sources: Karras, Common Women; R.I. Moore, The Formation of a Persecuting Society; Barton, Conquerors, Brides, and Concubines: Interfaith Sexual Power in Medieval Iberia

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^1 Karras finds one case of a man who cross-dressed as a woman and offered evidently non-penetrative sex for hire, since the people who testified against him in court claimed they had been fooled. (IMHO, Karras is too sharp not to have mentioned the other possible interpretation if the source left an opening for it.) In 15C Speyer, the charges against Katharina Hetzeldorfer included that she dressed like a man and hired (female) prostitutes for sex.

As a side question, would men in this time (and geographical area) have been able to rape the average woman without repercussions?

Edit: I'm genuinely curious if there was precedence for women ever being able to achieve any sort of cultural or lawful restitution in 1300's Europe. I do not condone rape.