One patient, Mikayla, 28, who asked to be identified by her first name to protect her privacy, drove from Texas to an Albuquerque airport hotel to use the service , and allowed The New York Times to observe. During video medical consultations, a nurse practitioner and patient care coordinator discussed effects like cramping and bleeding and urged her to call their 24-hour nurse hotline with questions or concerns.

After she received the medication, the process took a different turn. Via Zoom, a minister prompted Mikayla to look in a mirror to reflect on self-empowerment and recite: “One’s body is inviolable, subject to one’s own will alone.” After swallowing the first pill in the two-drug regimen, Mikayla recited a tenet about prioritizing science. The minister advised that after the pregnancy tissue was eventually expelled, Mikayla could recite: “By my body, my blood. By my will, it is done.”

Legal experts said some religious freedom lawsuits seeking abortion rights might succeed, given recent Supreme Court decisions that “supported religious exemptions even in cases where there are really strong health and safety issues,” said Elizabeth Reiner Platt, director of the Law, Rights and Religion Project at Columbia University. Arguments for exemptions might also be persuasive because most abortion bans have some exceptions, like rape, experts said.

“These should be very strong, compelling cases, but I also acknowledge that this is a highly political issue,” Ms. Platt said.

Josh Blackman, a professor at South Texas College of Law Houston who has criticized the lawsuits, questioned the plaintiffs’ legal standing, saying, “A lot of these women are sort of making prospective claims that, One day, I might be pregnant, and one day, I might have this problem and that might require me to have an abortion.”