Hmm. Can you run another service like https://github.com/vhiribarren/docker-echo-server on udp 53? If it fails, can you bind another port, both under and over 1024, with success? That would tell us if it's something with that image or a system problem.
Edit: I remember when I was running pihole under docker, maybe this? Not sure if anyone has mentioned it: https://github.com/pi-hole/docker-pi-hole/issues/968 (the NET_ADMIN capability is different from running as root).
Maybe also try starting the container without the port maps in the compose file to see if that works?
Also what network are you using? I think I had to put mine in host networking.