In a few years, Olgert Bardhi’s skills will be in high demand. A first-year resident in internal medicine at the University of Texas Southwestern Medical Center in Dallas, he’ll be a full-fledged physician by 2025 in a nation facing a shortage of primary care doctors.

The trouble for Texas: Because of the state’s strict antiabortion laws, Bardhi’s not sure he will remain there.

Although he doesn’t provide abortion care right now, laws limiting the procedure have created confusion and uncertainty over what treatments are legal for miscarriage and keep him from even advising pregnant patients on the option of abortion, he said. Aiding and abetting an abortion in Texas also exposes doctors to civil lawsuits and criminal prosecution. ...