Docker docs:
Docker routes container traffic in the nat table, which means that packets are diverted before it reaches the INPUT and OUTPUT chains that ufw uses. Packets are routed before the firewall rules can be applied, effectively ignoring your firewall configuration.
We use Firewalld integration with Docker instead due to issues with UFW. Didn't face any major issues with it.
I also ended up using firewalld and it mostly worked, although I first had to change some zone configs.