Want to know a fun fact about women in the US? They comprise half the population and they’ve got the right to vote. Pissing them off en masse is a risky political move –as Republicans are quickly finding out. A few months ago it looked like Republicans would decimate the Democrats in the midterm elections in November; now they are on much shakier ground. A recent Wall Street Journal poll found that 60% of voters support abortion rights in most or all cases, and that the supreme court overturning Roe v Wade earlier this year is “the single issue most likely to make them vote this November”. In the two weeks after Roe was overturned, the number of people registering to vote increased by 10%, new women voters far outnumbering men.

Cue furious back-pedalling from the right on women’s rights. Numerous Republican congressional candidates have removed or amended references to abortion from their online profiles in recent months, the Washington Post reports. Colorado state senator Barbara Kirkmeyer, for example, no longer refers to the “sanctity of life” on her campaign website. Arizona senate candidate Blake Masters has also been hitting the delete button. In an interview this year with a Catholic news outlet, Masters compared abortion to “child sacrifice”, saying: “It needs to stop.” Last month he toned down his language and clarified he simply supports “a ban on very late-term and partial-birth abortion”. He also amended his website so it no longer proclaims he is “100% pro-life” and instead says: “Protect babies, don’t let them be killed,” followed with: “Democrats lie about my views on abortion.”

Minnesota Republican gubernatorial nominee Scott Jensen has similarly moved away from publicly espousing hardline views on abortion. In March, Jensen said in a radio interview that he would “try to ban abortion … There is no reason for us to be having abortions going out.” In a video released in July, Jensen said his previous comments were clumsy, and announced he supports abortions in cases of rape or incest or if the life of the woman is in danger. (Thank you, sir, very nice of you to suggest it’s OK for a woman not to be forced to give birth if she will almost certainly die doing so!)

There’s nothing wrong with politicians changing their minds; on the contrary, politicians should be commended for thoughtfully evolving their positions based on feedback from the people they represent. Sadly, I don’t think that’s what is happening here. What’s happening here is that a lot of Republicans are morally bankrupt idiots who are happy to tone down their rhetoric to win elections and are likely to rapidly revert to their extremist agenda as soon as they get into power. That’s what supreme court justice Brett Kavanaugh appeared to do, after all. Senator Susan Collins, one of the few Republicans to support abortion rights, said she would nominate Kavanaugh because he had reassured her that he was a big fan of judicial precedent and wouldn’t overturn Roe. Though others have challenged Collins’ account of what Kavanaugh said.

We’re often told abortion is a divisive issue. The thing is, it’s not. Poll after poll shows most Americans support abortion being broadly legal. Just look at Kansas. Last month the conservative state decisively voted to reject a ballot measure that would restrict abortion rights. (A “ballot measure” is a form of direct democracy where proposed legislation is approved or rejected by voters rather than legislators.) Instead of reflecting on what happened in Kansas, Republicans across the US are now working overtime to try to make it harder to pass ballot measures.

Republicans may be doing their best to suppress democracy but it’s not dead yet. “To those of you who feel that women are inferior, remember you were warned,” Republican South Carolina state senator Sandy Senn recently told colleagues. “I think it’s going to be interesting to see what happens in the November elections. Because this issue is huge. You don’t think that women will vote single-issue on something like this? Because they will.” The problem is, where there’s a will, there’s often a Republican way to subvert it.

• Arwa Mahdawi is a Guardian columnist