Ah yes, I bet thou can also skip the booting part when thou run software on thy compooter. And Jehovah (or an idol of thy choice) forbids any configuration or upgrade requiring a reboot.

Any domain registrar/hosting provider that does not require propietary software to run?

If thou dissect this even more clearly thou wouldof noticed OP asked about running a domain registrar or hosting provider, not using their service. Also the word was propietary.

Now, if thou excuse OP’s imperfect English thou can find a clearer description below:

one that can be used without running nonfree programs