@scops damn. That sucks that other players ruin the immersion, because in my opinion, that's what makes the game so great... though if you wanted to do just the story solo, you could sub to Fallout 1st and do it on a private world.
Most story missions aren't very hard and it's pretty enjoyable as a single player experience but I do recommend getting into the multiplayer at late game. There's usually quite a few people that run the endgame events and seeing everyone in their different painted power armors and using different types of weapons to complete a shared objective is such a cool feeling.