A few years after her marriage broke up, Aisha Jenkins started thinking about having a baby on her own. She used a leading sperm bank whose catalog contained hundreds of potential donors from which to choose. But when Ms. Jenkins, who is Black, narrowed the search down to Black donors, only six remained.

“That can’t be right,” said Ms. Jenkins, a 46-year-old project manager for a software company who lives in the Washington, D.C., metro area.