If you want the story to make sense, the antagonist should always have the same gender than the protagonist. An antagonist from the opposite gender can't be a rival for the protagonist, unless they both live in a universe where everyone is strictly bisexual without a single bit a preference for a gender or another. But to be interesting such universe should gave a reason for this bisexuality and not just pass through it like if it was something totally insignificant.
There's also the case where this antagonism don't reflect at all in the sexual content, in this case the said antagonist can be whatever sex. But then the player will just not care about it. How beating someone on [whatever task] can be more interesting that fucking everyone ? The players will just give up, going for a full carnal life, while the antagonist will do whatever he's good at.