Supabase - ~39K stars
- Designed explicitly as an open source firebase alternative
- Typescript based
- Docker support
Parse Server - ~19K stars
- JavaScript based
- MongoDB or PostgreSQL
- Has dockerfile
Appwrite - ~16K stars
- Written in JavaScript and PHP
- Docker based
- Realtime support across all services
- Advanced security features (virus-scanning, data encryption, auto SSL, rate-limiting)
- Cross-platform: supports Web, Flutter, Desktop, Mobile and backend - over 10 SDKs: https://appwrite.io/docs/sdks
- Cloud Functions with +15 runtimes in multiple languages
nakama - ~5.4K stars
- Go based
- Has official Docker images
- CockroachDB (or another Postgres wire-compatible server)
- Designed for use with games
nhost - ~4.2K stars
- Written as a firebase alternative with GraphQL support
- Typescript based
- Includes docker-compose example
Kuzzle - ~1.1k stars
- JavaScript based
- Elasticsearch as a NoSQL document storage
- Has Docker Compose file
para - ~400 stars
- Java based
- Has official Docker images
- Database agnostic
LoopBack 4 - ~4k stars
- More of an api development platform than a BaaS, added here because could be good starting point if developing own BaaS
- TypeScript and JavaScript based
CloudBoost - ~1.4k stars
- Last commit in Nov 2020
- JavaScript based
- Has Docker Compose file
- MongoDB database
Apache Usergrid - ~1k stars
- Last commit in Dec 2020
- Java based
- cassandra database
SkyGear - ~400 stars
- Last commit in Jun 2020
- Seems v. complete but not many users (harder to fix issues)
- Go based
Platform as a service? Is one needed alongside BaaS? Dokku markets itself as mini heroku, maybe a good one to try first (e.g. Flynn, tsuru, openshift, dokku, cloud foundry)

Appwrite - ~15.7K stars
https://appwrite.io