BOWIE, Md., Jan. 26 - Sixteen months ago, Andrea Brown, 24 years old and unmarried, was desperate for an abortion, fearing the disappointment of her parents and the humiliation she might face. While frantically searching the telephone book one day, she came across the Bowie Crofton Pregnancy Center and Medical Clinic, a church-financed organization that provides counseling and education about sexual abstinence. The receptionist told Ms. Brown that the clinic did not perform abortions or make referrals but that she could come in for an ultrasound to make sure her six-and-a-half-week pregnancy was viable. When she did, everything changed. "When...