I think that's true for male nurses, but at least in my country male Kindergarten teachers often have a hard time.

Parents not wanting their daughter to be touched (or even helped to the toilet) by the male teacher, female colleagues making "jokes" about pedophile leanings, and so on.

The divide in typically female and typically male professions is not a one-way street.

I know a male nurse, and he's constantly getting jibes from patients about being gay. He's not, but that's kind of beside the point; the point is that there do exist stereotypes about male nurses that need to be addressed.

What did doctors and lawyers do starting back in the 80s? We should do whatever they did, since it seems to have worked.

A heavy dose of affirmative action. At least in the law field. From what I've been told anecdotally is that women and minorities are not held to the same standard as white men. They are accepted even if they are less productive and women are allowed to work fewer hours to deal with child rearing.

Why are you assuming we didn't?

Best is to do what symphony orchestras have done. All auditions are done behind a screen so you can be judged purely on your talent. You are not allowed to wear shoes to the audition because we don't want to judge your foot steps into the room. Just your instrument (which might be borrowed!) - and possibly your choice in music (or possibly not).

Of course music is easy to do blind this way. It isn't clear how you judge technical people in a fair way in a 5 minute audition. (see plenty of previous discussions here on white board coding)

Music also has high numbers of minorities going into it in the first place. The number of females who start a technical degree program is very low, and this is reflected in the graduations numbers (I understand females are more likely to drop out of the program as well, which needs to be addressed)

Failing that, what lawyers have done is a possible answer.