The Dobbs decision will lead to massive defiance of the law, in states that prohibit abortion. Women will still seek and obtain abortions - and they will be assisted by other women (in those states and in states that allow abortion), largely by provision of drugs for medication abortions.
Additionally, it's now just a matter of time until we have here an equivalent of the Savita Halappanavar case in Ireland - where a woman having a miscarriage is denied life-saving treatment, because the dying fetus "has a heartbeat," until the woman develops sepsis and dies. Physicians will be so petrified of possible prosecution for removing a dying, but not yet dead, fetus, that they will allow the mother to die - and of course the fetus will have died by that time anyway.
Some religious zealots will profess that this is "God's will." Of course, such zealots have a direct line to God, and understand "God's will" more clearly than the rest of us.
Expect some Jewish women to file religious freedom lawsuits demanding access to abortion - which Jewish teaching not only allows, but mandates, in situations where pregnancy threatens a woman's life. Expect our "religious freedom" advocates to tie themselves in knots to oppose these Jewish religious claims. Hypocrisy is not a limited phenomenon.
Also, expect a substantial, and growing, backlash against religious institutions in general - against the Catholic Church, against Evangelicals... and frankly, not undeservedly. These people are, of course, entitled to their religious views about abortion. But they have failed to persuade the American people that their views are right, that abortion should not be tolerated. Instead of persuading the people of the rightness of their moral position - because they have failed to make the case - they have chosen to shove their views down the throats of the majority of our people, who they have failed to persuade. There will be a price to be paid for that - a substantial and ugly price, I fear.
As a side "benefit" to decades of working to pack the Supreme Court with "pro-life" Justices, these people have also given us lots of other gifts - Citizens United, which opened the spigots of huge amounts of anonymous corporate money to politicians; the emasculation of the Voting Rights Act; Heller, and now Bruen, which make it next to impossible for states to protect their citizens from people with guns; and (in all likelihood next week) West Virginia v. EPA, which will cripple the Clean Air Act and Clean Water Act, make it effectively impossible for the US to respond to the climate crisis - and depending on the breadth of the decision, possibly cripple all sorts of other federal Executive Branch regulatory agencies (can you say FDA? CDC? USDA? OSHA? SEC?).
The "pro-life" zealots have sown the wind. All of us, I fear, are about to reap the whirlwind.