The only barriers to ANYONE becoming a pilot, or anything else in this country are money and competency.
Competency will follow a normal distribution.
Which bring on the topic of, should certain flying scholarships be available only to women? (I say no, that is discrimination).
As an aside I am currently doing further study on a subject I previously qualified in 35 years ago, agricultural science, when there were ten guys to every girl. Now there are about 20 girls to every guy. Just an example of how things have changed and "it's a man's job" is not only illegal but very old fashioned to say.