"What barriers are in the way to closing the gender gap in STEM?"
There are no legal, structural or systemic barriers in place for women's education or employment opportunities in the Western first world. All women have equal access, opportunities and freedoms to choose any and all professions, occupations, vocations or anything else just like men do. It is illegal to restrict women this way by laws that specifically mention women as a protected group that can not be discriminated against.
Some feminists have insisted that "society" is to blame for giving women certain messages. But "society" has no legal authority or dominion over women. Women are free to ignore or shut out any influence of "society". If any person, including any woman, is actively NOT exercising one's complete freedom due to these unauthorized "societal pressures", then that is a personal problem that they need to get help with, to overcome these personal barriers.
All adult women in the first world have complete freedom and autonomy to do whatever they like within the confines of the law .... just like men.