I'm not sure if I got this right and assuming this doesn't changed randomly on each game, it seems each society has its own early game action that unlocks it, so which of these actions you do first in your game will determine which society you get.
- Hermetic Order is unlocked by discovering a Natural Wonder;
- Owl of Minerva is unlocked by sending an Envoy. I assume the envoy you get when you are the first to meet a CS counts;
- The Void Singers is unlocked by discovering a Tribal Village;
- They don't show the Sanguine Pact, but I'll assume it unlocks by discovering a Barbarian Encampment, since that fits the pattern and the militaristic theme of this society.
So, early game exploration got a twist. Now you should care about what you discover first out of these four things. Tribal villages, City-States and Barbarian Camps are more likely to be the first thing you discover, so the Hermetic Order will be a rare society to get, compared to others. If I'm right about the Sanguine Pact trigger, you can play with Secret Societies but remove vampires if you turn off barbarians.
Edit: You aren't forced to use the governor title on the secret society, so that opens up the option to unlocking a governor earlier than we usually do.