I'm running Artix Linux with dinit and worry not, Mullvad does work. It just needs an additional step. I followed the instructions from this Artix forum topic, so I can vouch for that. I later discovered I probably could have just installed this AUR package, but I never tested that. The AUR also seems to have packages for runit and openrc, if that's more your speed. You may want to do a test run in VirtualBox or something.

Anyway, good luck!