in urban fantasy or paranormal fiction, the stories usually revolve around 'people' that are not really your normative next-door-neighbour 'people'... ergo, 'paranormal' or 'fantasy'... both are sub-sub-genres of a HUGE genre in fiction - 'fantasy fiction', which also goes by the name 'speculative fiction'...
so, your leads in urban fantasy and paranormal fiction - and in cases where its not necessarily leads, its the supporting characters - can vary from vampires, shifters of various kinds - so that's all the cat family, wolves, hyenas (which are considered belonging to both wolves and cat families), rats and bears even - to wyr - that's your fantasy generic term for what common folk might call dragons/ griffins or gryphons / unicorns, etc... - to magic-users, witches - or what in geek-talk are called 'wicca' (go figure!)- and sorcerers, revenants, zombies, ghouls, ghosts, erstwhile gods, and fallen angels and what not!
so here's the thing.. your first premise - the world humans live in - yes, humans and not 'people' - is very different to say the least... most books in these genres will hardly feature humans, and when they do, the takes on humans vary from ridicule and spite, to pity or nostalgia, to indifference or mockery, to anger/rage and the need to avenge the humans for the millennia of social ostracism, torture, and killings of what humans considered 'abnormal' or in other words, 'monsters'...
so all of the paranormal beings are abominations in themselves... now, i'm disregarding the fact that recent teen/young adult pop fiction would cry hoarse to prove otherwise - what with sparkling vampires and six-pack-abs-wolf-boys - or that in most fantasy/paranormal books, this 'being-seen-as-abomination' is taken to task; and its usually humans who are depicted as narrow-minded fanatics who have launched century-long crusades against these 'abnormal' beings that are neither human nor animal - in short, they're worse.. abominations..
now, your second premise - aka the oxymoron paradox - in many books i've read in these two sub-genres, the lead is usually not fully monster, nor fully human, nor fully anything... in short, they're half-breeds or hybrid monsters. if the two terms 'hybrid' and 'monsters' were earlier seen as synonymous, in these books, the half-breeds are themselves abominations... abomination within abomination, ergo the oxymoron paradox.
most world building and plots in UF/paranormal books, when not concerned with humans so much, often engage in meticulously weaving out the socio-political systems and structures of the characters... so vampires and ghouls usually function with a rather feudal 'master'-'servant' or king-subject dynamic; shifters and wyr have the pack leader, aka the alpha, and the rest of the pack, witches have covens, fallen angels are tied to the gods that rule, and so on, and so forth... and needless to say, most books, have brilliant takes on these social and political structures... so there's shifters who find the pack-lifestyle stifling, or vampire subjects who wish to be freed from their masters.. and so on..
and in books featuring half-breeds, one of the most fascinating aspects of the plots is in the severe disdain expressed by the half-breed/hybrid monster towards those 'pure-breeds' who are puritans... or in other words, if you haven't caught the drift by now, those pure-breeds who believe in the 'purity' of their blood/kind... of course, most often this sentiment is reciprocated by the pure-breeds as well... who persecute the half-breeds as abominations...
in fantasy fiction, this is most popularly recognized in the harry potter series by j.k. rowling... one of the main characters, hermione is a 'muggle' - a human-born girl who has come to wield witch powers... and the supreme villain of villains in the series - he who must not be named - is a pure-blood, born of witch and wizard parents, and believes in the purity of the witch-wizard race and sets out on the task of cleansing the world of such muggle-borns... eh.. similar, what say, to what has happened so often in human history?
so, to end, let me say that there's a way in which the half-breeds/hybrids here, often find a way out, to not just tackle the persecution and so on, but that it is in the very 'half'-ness of them that they discover their strengths... or their opponents weakness...
more on this, and what it might mean, with some examples, next time...