Competition, apart from rules, aint about fairness. It's about who's better. As of right now, women in athletics are basically about being the best among a weaker group. I say let them compete with dudes, even if they never get to be the best. Sports is all about who can win anyway, might as well widen talent and competition pools as far as you can.
As for locker rooms, they can keep that secret or integrate them. In most depictions of the future in sci fi there are integrated baths and shyt. I'm skeptical of that ever working because people are grimey as fukk, but maybe some day when we're all comfortable with our bodies it'll be different