Just saw at least 30 African American kids at the most recent AYSO Extra tournament in Riverside. Approx. 8 different teams, mostly girls teams. I usually see 1-2 Asian kids per team as well. If they so choose, they play. The boys might be different as I'm usually watching girls games with other parents and their kids. I think it is more a reflection on what sports they have grown up with and what sports they want to play, not a lack of access.
The ability to do things by yourself make soccer and basketball easy sports to get into. Get a ball, find a wall. My daughter dribbles a basketball at least 45 minutes every day, plus she is playing with the soccer ball another 45 minutes every day. She loves it, and can do either on her own, at almost zero cost. At her middle school basketball and soccer are two of the sports they play at lunch time. 5 times a week, 40+ weeks.