Probably not as the only system, but maybe give XP for living up to their cultural ideals (rather than just the obligations, which have narrative penalties for not doing).
What I mean is, every time a player can cite one of their gender's beliefs (so: 'Violence is always an option', 'No-one can make you do anything' for men, 'There is always another way' (and maybe 'she sleeps, she is not dead', somehow? Maybe to keep hope alive?) for women), and acts accordingly, they get xp.
Up to you, I personally just like 'soft' inducements to act in the 'culturally expected' manner than in the 'objectively most effective' manner.