Now with that in mind, would you hire someone that didn't have a degree?
A degree is a basic filter. How do you prove you have some knowledge about computers and programming? Traditionally it's a degree. If someone already has a bias that women can't program, the chances that she'll land an interview without a degree is slim to none.
In any case, a proper university will teach you the fundamentals. They will give you tools that will help you continue learning in the future, like how to recognize categories of problems, and a general sense of how things are abstracted from high level languages down to the bare metal. Learning "practical" knowledge of current languages/frameworks should be easy after that.
If I'm hiring for an open developer position and they have no degree (in CS/Math/Physics), it's usually a red flag for me.