One of the most effective ways to stop abortion is to dry up the supply of abortion providers. This happens to a large extent by itself, as the already relatively small band of abortionists grows older and young doctors seem more reluctant to use their skills to destroy babies. However, the abortion industry aggressively recruits doctors for its purposes. Incidentally, this is a major reason for their push toward chemical abortions.
There are a number of things the pro-life movement can do to see to it that although abortion is legal, fewer and fewer people will be willing to provide it.
One of those things is actually a very old practice in the Christian world: admonish the sinner. This is one of the spiritual works of mercy. An aspect of charity is to alert the sinner to the harm that sin does to him/her, as well as to the victim. In fact, the Second Vatican Council, in the Pastoral Constitution on the Church in the Modern World, says that crimes like abortion do more harm to those who practice them than to the victims themselves!
Abortion is a public activity, and is publicly advertised. There is nothing against charity to publicly call for prayers for the abortion provider, by name, and to publicly call upon the abortionist to repent.
The demands of charity in this case include being absolutely sure that the person in question does in fact provide abortions, and saying nothing untrue about the person. They also include making it clear that we in the pro-life movement and the Church always have the door open to those ready to repent of child-killing, as so many have already done. Approaching the individual, and providing opportunities for confidential dialog, are activities that also need to be included.
Besides the repentance of the individual, however, there is another side to the activity of publicly admonishing abortionists that the Church cannot afford to ignore. Even when a particular abortion provider does not repent, the public identification of that person as an abortionist sends a clear signal to other abortionists and to those in medical school who might consider becoming abortionists: Perform this activity, and you will face the spotlight, with all the discomfort that entails! We have evidence that this works in dissuading actual and potential abortion providers.
One thing the abortion movement can never do is to remove the stigma from abortion. When we point out that specific people perform abortions, we capitalize on the biggest weakness of the other side.
It is interesting that many who perform abortions do not want to be called abortionists. Those who practice psychology are called psychologists. Those who practice neurology are called neurologists. There is nothing unusual, therefore, if we call those who practice abortion abortionists. The difference, of course, is that abortion carries a stigma which no amount of money or power can take away. That is a fact we should use to our advantage.