Instances can handle sign-ups the following ways:
I'm trying to get my friends to leave Twitter, so I compiled this list of instances on the Fediverse to recommend.
Disclaimer: I can't guarantee the safety of every link on this site, they were fine when I wrote this, but I can't be held responsible for content off this site. Disclaimer over.
The order of these, inside of each category, is randomised. All of the instance names are clickable links. See the key on the left-hand side (or on the bottom, on mobile) for details. Descriptions, where applicable (for instances that aren't general purpose) describe what an instance is orientered towards (i.e. art, games, etc). All of these instances, unless noted otherwise, are explicitly or implicitly progressive, left-wing, or similar. Due to safety considerations, qualities such as "the admins are trans" or similar aren't listed (this is a publicly accessible website).
I know/trust the admin teams well enough to recommend these as good instances that probably won't turn out to be secretly horrible.
As far as I know, these are okay, but I don't have extensive experience with them and can't vouch for them – your mileage may vary.
These are under-moderated (by lack of staff or due to weird ideas about what doesn't count as bigotry) or otherwise not a great place to be.