Naeemah Khabir, a 35-year-old devout Muslim who works for the Department of Veteran Affairs in Philadelphia, has attended matchmaking events from New Brunswick, N.J., to Queens, N.Y. She has used several matchmaking services. Khabir, of Elkins Park, who has a master’s degree from Syracuse University, even hired a private matchmaker for nine months until the counselor assigned to her conceded that race was part of her problem.