Hmmm well not exactly. The bookclub just says which routes you have to finish by then to participate. So if you read fast, then you can take whichever route order you want~
Otherwise, then yeah, you might need one if you don’t wanna bother trying out choices until you get it lol.
As for route order, it doesn’t really affect after story. (AS spoilers) only the choices you make in your playthrough of Nagisa’s route make a difference
However you do need to collect the “lights” to reach after story, and those require some routes to be finished before others.