Okay, I'll bite.

So the first thing about a lot of explicit language, as proven by your examples, is that they often refer to religious mythology. Damn(ation), Hell, invoking Christ etc. I reckon this came about because, by referring to one of the most sacrosanct pillars of their culture, a person can make a point of how grave a factoid or situation is, or how strong their feelings are.
Here's the catch though: We don't know a whole lot about Bloodborne's religion, in spite of how central the church really is. Like yeah we know that they're all about blood healing, and presumably they consider Great Ones to be gods of some sort, but other than that? We can only make the vaguest guesses what a typical sermon would look like, and have no idea whether or not Laurence or someone ever wrote a manifesto, a bible as it were, or what kind of teachings the church imparts upon its flock. From the knowledge we have they seem more like a business than a church, if you ask me (exchanging blood healing for either monetary compensation, or service time). This makes it hard to pin down just how "spiritual" the healing church even is, and thusly also makes it difficult to imagine what sort of mentality and ideas it puts into its followers - which, to come round again, makes it challenging to come up with suitable expletives referencing all of these unknowns. So your guess of gods, blood and beasts is fairly accurate. Given the great problem that beasts pose, I reckon they'd be an excellent object to invoke in order to express disfavor.
Moreover, I think disease at large is a thing that Yharnamites are very cognisant about. After all, it's a city of sick people who came for treatment. An epidemic ravaged an entire district so badly it had to burned down (in recent memory!). The plague of beasts is a constant. Disease is an ever-present companion of the citizens, and is unlikely to be seen as pleasant. Calling someone sick, or saying a thing makes you sick, or calling a problem or behavior a disease or naming someone a blight - I think all of these are fairly believable ways in which a Yharnamite might swear.

In spite of being comprised of to a large extent of outsiders, it seems Yharnamites are quite xenophobic from what snippets of dialogue I can pick up. Thusly, I don't think it's far-fetched to imagine that they might be prone to invoking bigoted, xenophobic slurs to insult people, be they ethnical or cultural in nature. It's human nature, unfortunately, to judge others to be greedy or lazy or plain evil, simply because they share superficial traits with some prominent examples of said behavior. In a city of miserable exiles and outcasts, it seems very realistic to me to imagine that all of these people brought their grudges and prejudices with them, and let them simmer and stew in this crucible of human hatred. That said, the population *had* a bit of a reset after the events of the game, so maybe it's not quite as bad.

Lastly, I think some of the less culturally specific expletives always work regardless of context - the ones that refer to the lowest common denominator. Those referencing sexuality or excrement, things that are universal about humanity. Small variations occur depending on a culture's specifics, such as its tolerance towards deviancy (homosexuality and otherwise) or its degree of sexual freedom (for example the point at which one might be able to call a woman a whore - in some cultures, showing too much leg might be enough, in others it's adultery, etc). We don't have a whole lot of info on Yharnam's specific tolerances here, although if I were to hazard a guess, I'd say the city is relatively conservative (since, for starters, we're looking at repressed Victorian England as a base model). Also, and this is specific to the game, I think the purity of women is something that is very important to females in particular. Both Arianna and Adella consider their blood or themselves to be lowly, the old man is quite clearly not impressed by Arianna and her profession, and there is an entire can of worms that can be opened up on the subject of pregnancy, menstrual blood and so on, and their importance to Yharnam and its people. I have no doubt in my mind that a virgin is valued more highly than a woman who isn't, so I also have no doubt that a particularly promiscuous woman would be seen with disdain - and implying that a woman was one such, be a grave insult. And, as is often the case in society, I also doubt that this extends to men in any comparable fashion.

Sudden stop but ay, here's some food for thought lol

Edit: Actually, does the universe of Bloodborne - or, at least, Yharnam - recognize the institution of marriage? I'm honestly too lazy to look up the text surrounding Viola and Gascoigne because I feel there is probably an answer there somewhere, but I don't remember reading the word wife, husband or marriage anywhere in the game. Also interesting to ponder.