Why would race makeup be affected? We're talking about the gender gap not the race gap. Unless women in tech are more diverse race-wise than men in tech.
And, BFOQ isn't relevant here because there is qualification that is relevant - it's just that if men are getting under paid/left behind, then merely offering a low salary would be enough to attract them.
Any business that doesn't make an effort to hire more women than is strictly economically efficient is begging to get sued. "We have very few women because men are cheaper" won't get them out of trouble. The mere fact that women are underrepresented in that company will be taken as proof of illegal discrimination.
How do you figure? According to the law, race is never a BFOQ. Even if that weren't the case, this wouldn't be a BFOQ situation anyway.