A federal appeals-court case heard Wednesday in Ohio could help shape a contentious question in abortion law: Should a woman be allowed to terminate a pregnancy because of the fetus’s disability, race or gender?

The full Sixth U.S. Circuit Court of Appeals is considering the validity of an Ohio law that makes it illegal for a physician to perform an abortion on a woman whose motivation is fear that the fetus has Down syndrome. Abortion opponents say the case is winnable in one of the nation’s most conservative legal venues...