I don't think intention matters. For two reasons: The material effect of the bias is what is being evaluated and is more important than the intentions of the person acting on the bias, and assigning intention is always fraught with post-hoc rationalizations because human beings have limited access to their own internal behavior, let alone the behavior of an ensemble of humans.

There have been numerous stories used to justify the systematic and institutional biases and injustices against women throughout history: whether it is appeals to the divine order set forth by God, or appeals to the biological inferiority of women or the insistence that there is actually a structural bias against men and for women throughout society because, nominally, our institutions discarded explicit affirmations of male superiority and took up explicit goals for gender equality.

Bias is bias and it is out of fashion to insist that women are inferior to men. So I would not be surprised that the personal stories we tell ourselves to justify our biased actions avoid that rhetoric and take a different tack. Racists insist they are color blind and people who talk about structural racism are the real racists. A similar logic holds in gender politics.