I don't know about that. The comics that the movie was loosely based on where the original Old Man Logan story arc and X-23: Innocence Lost (Laura's origin story). OML was a lot more nihilistic and violence for its own sake. Laura's origins in the movie were actually significantly bowdlerized from the comic (if they adapt that comic into a movie, it needs to be R -- and I say that as someone who doesn't want R-rated superhero movies). While I'm sure that the tones influenced the R-rating, in all honestly, I think they could've taken out the F-bombs and blood and been able to tell the same story in a PG-13 film (baring James Mangold's observations that the studios would've demanded a more conventional superhero movies with the lower rating and possibly less focus on how violence affects those involved).
Others may disagree, but in all honestly, I think that the story itself isn't the reason for the R rating, but the language and violence.