Re: CC versus Joja specifically, if you start the Joja route you cannot get the
Stone Junimo Statue that spawns behind the community center every year. (I know that wiki article implies that you can only get a second one if the first one is destroyed, but that's incorrect, you can get one each year. I've seen someone get multiple of them.)
On the other hand, as Hill Myna mentioned, you can only buy Auto-Petters if you go through Joja. If you go through the Community Center, you can only get them from rare monster drops when you have a specific quest active, or rarely from treasure chests in a location you haven't been to. Without being too specific about mechanics you may or may not have seen yet, this basically requires you to get a
lot of staircases (the craftable item, I mean). By a lot, I mean that a full chest is about 36,000, and you need several full chests to get 999 Auto-Petters.
Technically another option is to sleep through 999 years without finishing the community center and without starting Joja, collect a stone junimo every year, and then go Joja to buy auto-petters. However, there is a lot of stuff locked behind finishing either the community center or Joja.
Or you could just give up on the stone Junimo statue. It's your challenge, nothing preventing you from declaring that certain items aren't fun and therefore don't count.