Some dictionaries list the phrase in the generic form of 'Suit oneself' (e.g. Merriam-Webster). Although I have come across the phrase 'Suit yourself' many times, I haven't seen any example usage for other reflexive pronouns like themselves. Is it possible to use the phrase like 'Suit themselves' to mean 'I don't agree but they can do whatever they want'?
No: "suit themselves" is not a grammatical sentence.
Suit in "suit yourself" is in the imperative mood: it's telling your interlocutor to do something. You can only tell someone to do something if you are addressing them directly. The reflexive pronoun yourself refers to the person you're addressing.
With themselves, you are talking about people, not to them. So you can't use an imperative verb. You would need to say something like "They can suit themselves," using an indicative form.