I did find some bins that have people hosting them publicly already, but due to the nature of this community they are probably going to advertise self-hosting as an option.
- https://privatebin.info/ is used as the pastebin alternative in the Libredirect extension. This page has a directory of instances.
- https://paaster.io/
- https://bin.bloerg.net/
- https://lesma.eu/:help
- https://www.verybin.com/
- https://kpaste.infomaniak.com/
- https://paste.sh/
- https://paste.myst.rs/
- https://paste.js.org/

These bins below are more like Github Gist replacements:
- https://demo.opengist.io/
- https://drift.maxleiter.com/

This last option isn't quite open source, it only has a bug tracker on Gitlab and an open API for plugin development:
https://www.pastery.net/
edit: formatting for clarity