I don't recall the last time I genuinely cared about the story in any game. Possibly God of War? I thought the story of TLOU2 was meh mostly. It was semi interesting I guess. I usually skip cut scenes for side missions, because I don't really care why a character wants something done, just give me a marker on the map and list of objectives and leave me to it.
So far I have found the variety of ways to acheieve a task quite entertaining and engrossing.