Until they can pass laws to more directly ban the practice, they are looking to find ways to let the ACA's exchanges restrict private insurers from offering any sort of abortion coverage.
'HR7 prohibits insurance carriers from offering policies that contain abortion coverage on the exchanges set up under Obamacare to sell insurance coverage to individuals. It prohibits low-income women who qualify for a healthcare subsidy from receiving it if they purchase a healthcare plan that covers abortion. And it would withhold the small business tax credit from employers who offer policies with abortion coverage.'
Though it doesn't specifically target all insurance policies (since, so far, it can't), it does make it more likely that carriers will simply avoid the complexity of multiple parallel policies by simply dropping abortion coverage altogether.
Of course, this doesn't actually ban abortion. It just helps restrict it to people who can afford to pay for it out of pocket. How Gilded Age of them.
Republicans push ahead with plans to hinder insurance coverage for abortions | World news | The Guardian