Not really, but let's think together.
Sport is sport. Sport imitates the skills of war, at least in olden days, and the tradition continues with athletics.
Sport does not imitate reality.
The reality of war doesn't care if it's a woman or a man out there on the wrong end of a bullet or a bomb.
They say that's why women were not in traditional combat roles, when the objective was to win at all costs. The women combatants would become pawns in the enemy's strategy. Raised right, Americans would move to protect the women at their sides and thus threaten the mission, in theory, back in the olden days of the greatest generation.
Feminism tampering with reality has lessened reality into the war of the sexes, so a man better watch it if he holds the door for a woman, for he might be inviting gender bias, sex discrimination, lawsuit blah blah.
In the real world I've noticed that women are thrilled when I hold the door for them, smile, and graciously say please, after you.