Hi there! Welcome to the site
Fitz Jarro
As far as I'm aware, public threads are technically open to all, but sometimes they indicate that they are meant for members of a specific faction. Normally, they will say so in their title or the first post. In that case, I personally follow the etiquette of respecting the wishes of said group of writers. You might reach out to the original poster for permission to join if you would like to take part in the story even though you are not affiliated with their faction.
If there's no affiliation requirement like that, just write up a reply and jump on in!
I hope that helps!