Your friend breaks my heart. I wonder if a) yes her mother's shame rubbed off on her and b) she's taking the path of least resistance out of fear. I spent some time in the 90s just "being white" because it was easier. I really do feel like admitting her Blackness terrifies her.
Nobody ever worries about a child's skin being too light.
Like you, I'm proud of my Black heritage. I'll never call myself Black because my experience in the world is not that of a Black woman on a day to day basis. But I am a proud mixed race woman.
As for her having a baby, I question whether bringing a child into her self-loathing is a good idea, but it's not my choice or my business.
I feel sorry for her, she's missing out on such a rich and beautiful heritage.