Ah yes, I bet thou canst also skip the booting part when thou runst 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 dissectst 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

Like virginity, it's either with or without innit, or doth thou prefer thy olive oil lightly fucked?

static sites [are] not suitable for any business or professional use

I wouldn't agree with this statement, there are plenty of businesses and professionals who are only on the interwebs to share their contact, biography or product knowledge base.

That being said, there are VPS providers running on libre software like vpsFree.cz which I use and can recommend. There should be more out there but I don't keep track them, sorry.

There's much thinner chance there exists a registrar caring about thee or thy software freedom though. People at sr.ht, LLC talks about setting up one but so far it's just talks.

OpenNIC registrar (only be.libre seems to be functional) work without JS and thou can prolly ask them to license the site freely but non-ICANN domains are not practical for business or professional use due to the low adoption.

once

I get thy stand on this, personally I also have to compromise my software freedom to register my domains, but again OP asked to avoid X and saying after doing X you won't have to is not answering the question.

The question wasn't about avoiding installing but running proprietary software.

Gandy or namecheap

I'm pretty sure they require proprietary client-side scripts to function as well.

Its market share defeats the point of self-hosting.

If you have a static IPv6 address you can host your own authoritative DNS locally and use it for IPv4.

Remember when Reddit was the free software alternative?

My taste is mainstream enough that I just go with Wikipedia from artists I already know, and once a year, the Grammys.

Is it an aggregator? How about directly subscribing to web feeds?