Sadly you indeed do have to join one of them, the main scenario requires enlistment to continue (it is also a requirement for using mounts, as the chocobo license is an item purchased from the GC in company seals currency).

Don't worry though, once you've enlisted in one and gained the chocobo license, you are not required to have anything further to do with them, although there are bonuses and perks associated with being with one.