There is a social stigma, but, as far as I can tell, it seems to largely be a stigma between women themselves. Even if there is some wider social stigma, I don't think that it constitutes "being kept out."

There is a similar social stigma against men being nurses, but I wouldn't claim that men are being "kept out of nursing." It is just looked at slightly oddly by some and this leads to less male nurses. Why is there not more noise about this imbalance?

The whole problem is that all of the discussion around the issue of women in tech seems to focus on the problem way too late in the "pipeline". It is trying to address the symptoms after the damage is already done.

Trying to focus on hiring more women, as a goal unto itself, seems wrong to me. The problem isn't hiring more women. That leads to people hiring under-qualified women simply because they are women. The problem is that the supply is crazy low because <20% of Computer Science graduates are women in the United States.

So, if you want to fix this imbalance then fix the stigma. Perhaps have a marketing campaign that makes it seem less socially damning to be a girl hacker while they are an adolescent.