Do you depend on a DNS root server to map your website name to your IP address? That's a third party.
There are ways to remove that dependency, but it's going to involve a decentralized DNS replacement like Namecoin or Handshake, many of which include their own built-in alternatives to the CA system too so if "no third parties" is something you truly care about you can probably kill two birds with one stone here.
Registrar is the big one, if yours decides to do a Google and randomly ban you and automatically decline your appeal with AI, you're stuffed.
This is generally my biggest concern. Not that I'm doing anything shady, I've wanted to setup a potentially politically charged site in the past.