The pages of equivocation with the concept of "genre" are getting tiresome. The word "genre" can mean types of literature as broadly defined as fiction (a subgenre of fantasy, as My Name is Legion
instructs us,) or as narrowly defined as the prosody of the sestina. If you do not use the term consistently, it sows confusion at best. Or serves as spurious grounds for abusing someone.
Since the Western somehow emerged as the main set of contested examples, note that this "genre" is defined by its setting. Literally, this is the US West in roughly the 19th century. Borders were fluid geographically, and outliers into Mexico and Canada are trivial. A story from any other genre can be put into this setting. Richard Matheson wrote a horror novel set in the West, therefore it was a Western. It was still a horror novel.
This is not a contradiction, nor is it even a cross-genre or genre-blending story strictly speaking, because the horror genre is defined by its intent to horrify the reader (which imposes no proper form or setting on the writer,) and the Western genre is defined by its setting. The confusion arises from using "genre" to distinguish stories in different ways. In this example, by authorial intent and by setting. It's like trying to distinguish people by hair color and height. Saying someone is blonde does not contradict or blend descriptive genres when you also say she is short.
In another example, Dashiell Hammett wrote a couple of crime novels, Red Harvest and The Glass Key. Akira Kurosawa made a samurai movie based on these novels, Yojimbo. Then Yojimbo's plot was used in a Western, A Fistful of Dollars. The Glass Key was made into a movie and I read that Kurosawa copied a scene very closely. Nobody in their right minds would call The Glass Key a Western. But somebody could sensibly call A Fistful of Dollars a gangster film. They probably wouldn't because minds muddied by ill-conceived notions of genre would find it difficult to think so clearly.
The Western strictly speaking is a subgenre of historical fiction, which is also defined by its setting, the past. There is one difference, which is that the classic Western is not properly set in the past but in a mythological version of the past. Christopher
noted this but soon contradicted his own notion of the Western genre as defined by this mythology in his eagerness to quarrel with another poster. The mythological version of the West is notable for the absence of race as an internal problem for society. By the mythological standard, movies like Quigley Down Under, which are very much about race, simply are not Westerns by that standard either. And by the sound of it, neither was The Proposition.
A strong man saving society from chaos by restoring order through violence (very occasionally trickery,) is a genre common to the classic Western. It is not unique to the Western, however. The genres unique to the Western are things like sheepmen versus cattlemen, very specific to the setting. As in the case of Red Harvest slowly morphing into a spaghetti Western, the strong man story is a transfer from other scenes, such as tales of chivalry.
But it seems to me that the desire to label such stories modern or urban Westerns is an oblique acknowledgement or invocation of race in the threat of chaos. It's pretty overt in the very title of a movie like Fort Apache the Bronx. It's barely disguised in things like McCloud or Firefly. The real question is, does it help understanding to look at the classic Western mythology, then label something like Justified a Western? I think not. I think it sows confusion about a crime story to ignore the reality that race is an incredibly important aspect of criminal justice as practiced in the US today, by trying to trivialize it as just a romantic tale, borrowed from an innocuous genre.
Going back to SF and fantasy, these "genres" are defined by the internal rationale for the fantastic element. In the first, the fantastic is still somehow supposed to be natural, connected to our mundane world, most often by being set in the future. In the other "genre," the fantastic is supposed to be supernatural. There is a third possibility, that the fantastic isn't justified at all, but is blatantly absurd. This includes things like Flan O'Brien's At Swim Two-Birds, Kafka's The Metamorphosis, Jasper Fforde's Tuesday Next novels, Latin American "magic realists." If this stuff was all just fantasy, of course, the third category would be on the shelves of your "SF" section in the bookstore. It's not, nor do critics read them the same. So much for the ignorant idea that it's all just fantasy. But the point has always been, that in the case of SF and fantasy, the way these "genres" are defined preclude each other. Yes, even in this there will be the occasion genuine cross-genre or genre-blending exercise, for about the same reasons that people will utter or write oxymorons. Generally, by error, occasionally, for humor, rarely, for profound wit. But despite this, harping about the fludity of genre boundaries is much like harping on the possibility of uttering or writing sentences that contradict themselves, ignoring the large majority of normal sentences. The notion that some fantastic element is justified as somehow natural does not tell us much about what kind of "genre" as defined in other ways an SF story is. It's impossible to define SF as a genre in the same way you might define a mystery or romance. Like the Western it is unlikely that there is a "genre" (defined by narrative intent) unique to the SF "genre" (defined by setting, which includes some supposedly natural fantastic thing or person or place, etc.)