T HOUGH CONSERVATIVES are by and large taking a kicking in the culture wars, they continue to hold ground on one front: abortion. Americans increasingly accept the right of gays to adopt children and marry. But they have not moved in a similar direction on women’s right to terminate unwanted pregnancies. Abortion is as controversial as it was 46 years ago when the Supreme Court ruled it a constitutional right in Roe v Wade. Hence the success of “Unplanned”, a low-grade, blood-spattered film about an abortion nurse-turned pro-lifer that has become a box-office hit.

More significant fresh evidence of Americans’ antipathy to abortion comes in the form of legislation. In the first three months of 2019, 12 states introduced bills that ban abortion from the moment a fetal heartbeat is detectable. That happens around the sixth week of pregnancy, two weeks after a missed menstrual period, when many women do not yet know they are pregnant. In other words, the bills come close to being total abortion bans.

Around half have made it through at least one legislative chamber. In some states they have been signed into law. In March a “heartbeat” bill was signed by Mississippi’s Republican governor. Georgia’s governor, also a Republican, is expected to approve a similar bill there—sparking threats of a Hollywood boycott of a state that is a hub for film and TV production.

The rush of state-level heartbeat bills represents a shift in strategy by some anti-abortionists. Since 1973, pro-lifers have for the most part focused on chipping away at Roe by introducing burdensome regulations that make it harder to obtain an abortion. These range from imposing waiting periods between a consultation at a clinic and an abortion (which can be difficult for women in states with few clinics) to dictating the width of clinic corridors. This approach has been successful. The Guttmacher Institute, a pro-choice research group, says 401 abortion restrictions were introduced between 2011 and 2017. Eight states have only one abortion clinic.

Heartbeat bills, by contrast, are straightforward violations of Roe—and so liable to be struck down by the courts almost as soon as they become law. In March a federal judge in Kentucky blocked a heartbeat bill the day the governor signed it. A similar law was blocked in Iowa in January. Mississippi’s will almost certainly be halted before it comes into effect in July.

Pro-lifers are nonetheless persisting with this campaign in the hope of getting the Supreme Court to weigh in on the issue. Excited by the court’s new conservative majority, champions of heartbeat bills hope the justices may use one to overturn Roe—as Donald Trump promised them during his presidential campaign. As that suggests, Republican politicians are aware that merely dangling that prospect is a big vote-winner.

In reality, heartbeat bills are unlikely to achieve their promised goal. Mr Trump’s new justices, Neil Gorsuch and Brett Kavanaugh, are conservative Christians who hate abortion. But neither appears ready to overturn the 46-year precedent that Roe represents. And Chief Justice John Roberts, a conservative who has himself expressed scepticism about Roe’s legal basis, is anxious for the court to appear non-partisan.

It is more likely that the Supreme Court’s conservative majority will undermine Roe by upholding stringent anti-abortion regulations. Mary Ziegler, a professor at the Florida State University College of Law, says it may inflict the worst damage by agreeing that regulations do not create an “undue burden” on women’s access to abortion, the standard used by courts to determine whether restrictions are constitutional.

The court is expected to rule soon on one such law passed in Louisiana. It requires abortion doctors to have “admitting privileges”, or the right to admit patients to a nearby hospital which many hospitals do not allow and which, elsewhere, has led to the widespread closure of clinics. In 2016 the Supreme Court struck down an almost identical law in Texas, saying it imposed an undue burden. Chief Justice Roberts dissented from that ruling, though in February he voted to temporarily halt the law in Louisiana while the court decided whether to take it up. The other four conservatives voted to uphold it.