As long as you remain a foreign in these lands, we consider it a privilege to host you, my King :)
I agree they saw gods/myths as reality, particularly up to the 4th century BCE, when traveling around started to shake some beliefs out of them, and some new philosophies proposed a much reduced role for gods or unified them in a single force. But the game is focused on a single book from Plato's Republic. I don't want to add anything else, even if it would be realistic for the time the game is happening, in order not to distract from the main goal.
With regards to the female character... I don't think she would die immediately, she would instead be unable to succeed in politics. Maybe she would become the local oracle I mentioned somewhere else in the game comments.
Let's call her Lysistrata. I am thinking that, if you choose female, you become Lysistrata, a philosopher/diviner, but not a politician, and the game ends in frustration. If you chose a male character, you will encounter Lysistrata as a NPC. Maybe Lysistrata would actually know Socrates' philosophy, and annoy the male main character for being a tyrant in the making.
I do agree with you, there should be many paths towards victory. I do wish I had enough resources to make something really awesome: to create two alternative victory paths, one in which you reinstate the oligarchy (you win but the people lose) and one in which you reinstate the aristocracy (all win, according to Socrates). I am sure that I do not have the resources to do that as of yet, because each path would lead to at least 25% more cost and time, and I don't have those resources. But you are right: all initial conditions of the male character should be able to arrive at a victory, perhaps through a different path and with more effort and luck.
Cheers,
Pedro