If women will be in combat with men in the military, and have to go through the rigor of that training, there's no reason that they shouldn't compete along side men in sports. I teach at a small enough instutition that many of the sports are coed like tennis and soccer.
Using the current rules that are in place, women have no chance of competing with men in the NFL, NBA, or MLB. Obviously.
What specific rules in place prevent women from competing in those leagues?
The rules don't prevent them from trying to compete. They won't be able to compete athletically without changing the rules of the game.