When we create a game world (or a book, or movie, or whatever) we don't define everything. Some things we care about and some things we do not. So when I run a game of 3:16, I am being very explicit that I don't really care about having characters differentiated by how good they are at skills. I really only care about fighting, and not-fighting.
So when you elect to make a mechanical difference between men and women, you are stating that this is something that you are about, and you want players to care about. You are also forcing people who might want to play a non-binary character into a particular choice. So the big question you should ask is: Why do I want to highlight this?. Why do I want to enforce a stereotype? -- irrespective of the accuracy or not of that stereotype. Another way of thinking about it is to ask yourself "If I dropped this rule, would it make a big difference?"
For your example Conan game, do you really think it would make a difference if you dropped the rule? I'd guess most people who want to play a Conan game are going to naturally create characters that feel like they might be Howardian -- in other words the premise of the campaign pretty much covers the rule. The only people who are likely not to follow the rule would be players who are unhappy with the premise of the game (in which case, you have issues already) or people who are generally happy, but find something grating. You might have a person who doesn't want to overtly display gender and plays a robed, mysterious magician (Thoth-Amon of the Ring style). Does it harm the game to allow that? Is it better to say "You can't do that because rules" or to say "OK, give it a go, but remember that in Conan's world, gender is a big issue".
Summarizing, a rule is meant to make people pay attention, decide and to enforce a point of view. It's probably better simply to depend on the premise of the game.