It’s definitely doable. I run both gluetun & tailscale in separate docker containers on Ubuntu. The trick here is that gluetun should get /dev/net/tun device (basically the default example in the project readme) and tailscale should he configured (via env vars) to run in userspace mode
Surprised nobody has mentioned cloudflare ddns. If you registered your domain with cloudflare, you can use the api or qdm12’s (author of gluetun) ddns-updater to keep your A/AAAA records up to date.