Abortion foes behind the clinics known as “crisis pregnancy centers” want the U.S. Supreme Court to strike down a California law requiring the clinics to inform their patients about the availability of abortions. But if they win the California case, they could lose much more in 16 other states, where laws require doctors to tell patients that abortions could harm them.

The clinics, backed by nationwide groups opposing abortion, argue that the notification mandated by California — that the state makes abortion and reproductive care available at little or no cost — violates their freedom of speech by compelling them to “advertise” abortion and send a message with which they disagree.

But legal analysts say the same argument could be used against laws in states that require doctors to tell women that terminating their pregnancy would make them more vulnerable to breast cancer, mental illness or suicide, and that fetuses can feel pain.

The California law merely requires “disclosure of accurate information” about the availability of health care, said Deborah Rhode, a Stanford law professor who has written about gender discrimination. A Supreme Court ruling that the state cannot require crisis pregnancy centers to pass along that information “would surely cover speech that has a far less justifiable reason for protection,” she said.

The abortion-warning laws mandate “adversarial-argumentative statements” that surely have less constitutional protection than the notices California requires, said Jesse Choper, a UC Berkeley law professor and former Supreme Court law clerk.

To the contrary, said Mat Staver, president and chief attorney of the conservative Christian nonprofit Liberty Counsel, because crisis pregnancy centers consider abortion to be murder, any message that opens a pathway to abortion “would actually take the lives they’re trying to save.”

The potential that the challenge to the California law could backfire, first voiced in the online Slate magazine by legal commentators Dahlia Lithwick and Mark Joseph Stern, raises the stakes for the case that the Supreme Court agreed to hear last week.

The California law, sponsored by Assemblyman David Chiu, D-San Francisco, applies to all reproductive health centers but was directed at more than 200 crisis pregnancy centers in the state. Those centers, many of them religiously affiliated, offer free counseling and services, including pregnancy tests, ultrasound examinations and parenting classes, to pregnant women, but steer them away from abortions.

The law, effective in 2016, requires all clinics that have a doctor on staff to notify clients of the range of reproductive health services available under state law, including contraception and abortion, and to list the phone numbers of the county’s social service center. Clinics without a doctor must notify clients that they are not licensed by the state.

A federal appeals court upheld the law in October 2016, saying the state does not violate freedom of speech by requiring clinics to provide accurate health care information that patients have a right to receive. But the Supreme Court granted a hearing of an appeal by multiple clinics and will decide the constitutionality of the law in the term that ends next June.

“The state should protect freedom of speech and freedom from coerced speech,” said Kevin Theriot, attorney for Alliance Defending Freedom, which represents the clinics.

That’s also the argument that medical groups and abortion-rights supporters have made against laws enacted since the mid-2000s that require doctors to advise women that the abortions they seek could harm them.

Five states require a warning that abortion increases the risk of breast cancer. In seven states, doctors must tell women they would be more prone to mental illness, which under some state laws includes a warning of the risk of suicide. Twelve states require doctors to tell pregnant women that their fetuses can feel pain.

Opponents of abortion say they have studies to support all of those warnings. But most scientists say otherwise.

A UCSF study, published in the Journal of the American Medical Association in 2005, found a scientific consensus that fetuses were physiologically incapable of feeling pain until the third trimester of pregnancy, when virtually no abortions are performed. The American College of Obstetricians and Gynecologists reached the same conclusion in 2012.

The American Cancer Society, the World Health Organization and the American College of Obstetricians and Gynecologists all say research has found no link between abortion and breast cancer.

Regarding mental illness, the American Psychological Association said in 2008 that its studies showed abortion may lead to feelings of sadness or guilt for some women but “does not pose a psychological hazard for most women.”

Nonetheless, a federal appeals court in 2012 found enough evidence, including medical studies, to uphold a South Dakota law requiring doctors to tell women that an abortion would make them more prone to suicide.

Other courts have limited or overturned some state laws designed to restrict access to abortion or discouraging women from terminating their pregnancies.

In 2014, a federal appeals court struck down, as a violation of patients’ rights, a North Carolina law requiring a doctor to perform an ultrasound examination on a woman seeking an abortion, display the image and describe the fetus to the woman, even if she objects.

A North Dakota judge in 2002 dismissed a false-advertising suit against an abortion clinic for its brochure that declared no proven link between abortion and breast cancer. A federal appeals court in 2013 struck down an Arizona law banning abortions after 20 weeks of pregnancy — a law based on the claim that fetuses can feel pain at that stage — though similar laws remain in effect in other states.

And in 2015 the Supreme Court overturned a Texas law that would have shut down most of the state’s abortion clinics by requiring them to meet the same standards as surgical centers, and by requiring doctors to have admitting privileges at nearby hospitals.

But no court has yet overturned a state law requiring doctors to warn patients about the asserted harmful effects of abortion.

That could change if the Supreme Court rules that California violates crisis pregnancy centers’ freedom of speech by requiring them to post information about the availability of abortion.

“There’s very little speech that you can compel by law,” said UC Berkeley’s Choper. “You can require an organization to give very basic information. I don’t think you can require an organization to make statements that are disputed. ... Those statements (about the harmful effects of abortion) are in dispute.”

Staver, whose Liberty Counsel organization represents another group of crisis pregnancy centers in California, said there might be a way to preserve the abortion-warning laws while overturning the California statute.

The pregnancy centers are “primarily doing counseling,” he said, and are being required in California “to speak a message that is opposed to the central mission of the organization ... saving lives.”

Doctors also have free-speech rights, Staver said, but probably can be required to pass along information to their patients that is “supported by some medical evidence ... generally accepted in the medical community. It would have to be considered on a case-by-case basis.”

Bob Egelko is a San Francisco Chronicle staff writer. Email: begelko@sfchronicle.com Twitter:@egelko