Do I have to join a GC to progress the main story?

[Tacti]

I'm looking at these three weirdos, thinking about the groups they represent, and I just... don't want to join any of them? They have daft hats and look generally weird.

I'd prefer to be independent from the factions while still enjoying the game and its story.

Their soulless expression doesn't help either, I mean, just look:

[Enkidoh]

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.

[Taika]

Also, you're not forced to wear the daft hat.

[Niwashi]

(it is also a requirement for using mounts, as the chocobo license is an item purchased from the GC in company seals currency)

A minor quibble here, but there is no licence for chocobos (nor anything else I'm aware of) in this game. Licencing was a big deal in FF XII and Tactics, but not in XIV.

It is true, however, that you need to be in a Grand Company to get your chocobo itself, as your GC will issue him to you (in exchange for some GC seals). And that once they've done so is when the game will unlock the Mount system, so that you can then use not only your new chocobo, but also any other mounts you have (though there is no in-universe explanation of that feature unlock).

[Canadane]

It's not a license but an issuance. But in effect acts as a general mount license.

[Renius]

The game wants to expose you to everything while progressing so this is just one part of it and you get a mount and the ability to ride from it.

[bounddreamer]

Til sea swallows all!!!

[Pintsized]

Also, if you ever want to be able to buy a house or an apartment or Free Company Private Room you need to reach the second highest rank in a GC as well as hitting 50 in a DoW/DoM class, and reaching that requires running non-MSQ dungeons and also possibly completing the GC Hunt Log; I'm not sure how much of it you need to do but I'm sure that some ranks in the GC required completion of GC Hunt Log tiers.