The actual movie was completely different from this. Full spoilers below the cut.
Rather than this Western narrative, the movie resembles much more a horror flick, particularly grindhouse, extremely gory films. There's more blood and visceral stabbing and body blows than in any other big superhero movie, including the supposedly "gritty" DCU movies. That cute little girl? A harpoon comes out of her chest Alien style, within the first 45 minutes. (It's ok, she get's better, she's a Wolverine.) And ninety percent of the mutant powers on display are just one of the three Wolverine characters taking a mortal wound and shrugging it off and continuing to go after their prey: it's basically a zombie movie. Perhaps the most cliche difference is that, despite the Western references like a eulogy from "Shane", instead of ending with the lonely cowboy riding off into the sunset, he dies, and the Final Girl is the only one of the original gang to make it to safety.
(Not to mention the scene where a platoon of soldiers explore an abandoned warehouse, as the wirey girl skulks through the shadows and the rafters and takes them down one by one. Or the remorseless killing machine that can only be stopped by ramming it with a truck.)
In fact, this movie most closely resembles a Mad Max feature, some combination of Fury Road and Beyond Thunderdome, with its gorefest fighting and dying world aesthetics. And like Fury Road, there is an initial obsession with escaping to a utopia, as being the only hope for our characters. (Utopia means "no place".)
Where Fury Road declares that hope is not redemption, and the response to the absence of Eden is to return home and take back all of society, for everyone - Logan says the lie of Eden (it was nothing more than a comic book fabrication) transmutes to truth if enough people believe in it (all of the escapees meet there and make a home together anyway).
Logan also tries to make a lot of pointed commentary about current American politics, but the references are so topical, on the nose, and awkward that they contrast badly with the more universal narratives.
- GMOs are mentioned as producing terrible tasting corn that we glug by the gallon as corn syrup drinks - and are how corporations managed to inoculate the whole population from becoming mutants. This is done in two isolated and intrusive lines of dialogue.
- As ever, the entire plot behind the evil corporate goliath is: produce super soldiers, and contain bad PR when the experiment goes wrong.
- The children-as-immigrants trying to cross the border into Canada replicate fears of ICE agents chasing innocents so much to try to distract us from "Why is Canada any safer? If they are such well-intentioned Justin Trudeau-descendants, why aren't they doing anything to help these kids only miles from their border?
- Racism against (upper-)middle-class rural black families is brought front and center... which is not very typical of how racism exists in America. As Chaw mentions, even water rights come up.
Contra all that, two of their pointed topical issues do use effective imagery
- Tractor trailers without drivers make a highway that feels inhuman, and can explode with violence the moment any hacker messes with the controls.
- Professor X having ALS and the threat he represents with that is quite depressing and even horrifying, when he paralyzes an entire city block.
This isn't all bad, and in fact the first two points can be read as satirical anti-plot, where the continuity obsessed fans of the MCU and Wookiepedia, find their entire world of "tactical realism" assaulted by egregiously bad or anti-climactic plot details. Aka Midichlorians. Other examples of this:
- Logan is dying due to his adamantium skeleton poisoning him, and the only way to kill a Wolverine is with an adamantium bullet to the skull, because ???
- Choosing to have dinner and stay the night with the innocent farming family very obviously puts them in the path of a murderous rampage.
- It appears the last of the X-men team was taken out by Professor X having an Alzheimer's seizure. Charles himself dies of a claw to the chest in bed, and receives no note of his passing except a blubbering, incoherent Logan pointing at the water. (In fact the mercenaries chasing Logan and the girl know full well the world's most telepath is with them, and just don't care.)
All of which is not necessarily criticism, but a demand to read the events in the movie purely on a thematic level, without seeing this as some "final chapter" in the X-universe storyline. And judging by reviews, that has worked rather well.
Once all that is out of the way and you're left with the well down horror film filmmaking, you remember that gorey flicks are often called "exploitation" flicks, and in fact this movie often feels like youthxploitation. There's this emphasis on the decrepitude of Charles and Logan, and the dying post-mutant world all around them, that can only be saved by the injection of the extremely youthful (innocent, energetic, pretty) Laura. She gets them on a road trip and acting like a family, and there's the hope that whatever mysterious origins produced her can save mutantkind, etc etc. She also kills a lot of dudes in awesome vengeance.
This even leads to Logan ingesting a drug that does make him youthful and vital again... which very quickly wears off and shortly thereafter he dies. None of their old world is saved, and the only real hope is someone starting anew again.