Sorry for the delay in responding.
John Cardinal O'Connor, former Archbishop of New York, answers your question in a 1994 "Killing Abortionists: A Symposium" sponsored by First Things.
The direct killing of the innocent is a moral species of murder. Some who oppose murder argue that the abortionist is really a "serial killer" of innocent babies. Indeed, a killer is one who acts, neither out of defense nor compassion, and not pro bono, but one who is paid to kill a moral innocent. Such people argue, further, that deadly force is justifiable against this "medical hit-man" because it will prevent him (or her) from killing more moral innocents.
This assumes many things that are not true.
First, this line of argument assumes that one can try to kill a potential killer to prevent more killing. But received Christian teaching repudiates that direct intent to kill. Justifiable self-defense applies only to that killing that is not directly intended, i.e., a result that is a secondary effect. For a good Christian explanation of legitimate self-defense, please see the Catechism of the Catholic Church (## 2263-2265).
Second, the justifiable defense argues that the guilt of a known intentional killing (of the abortionist) can be outweighed by preventing another, but as yet unknown, evil. But this offends the cardinal biblical principle that a good end does not justify an evil means (Romans 3:8). This kind of consequentialist argument is thoroughly repudiated in Veritatis Splendor (71-83).
Third, shooting the abortionist is not the same as killing in defense of home or family because the latter can be an incidental, unintended, secondary effect, whereas the shooting of the abortionist (according to reports) was intended, premeditated, and not an accident at all.
Further, those who kill on their own authority advance what all pro-life people oppose. When lethal force is used against the abortionist, is not the clinic guard free, and the police officer duty-bound, to repel that attack with force, even lethal force? Where does this spiral end? How is it limited?
Surely, we are all as tired of abortion as we are tired of murder. But we must fight murder without conforming to it nor condoning it; it makes no Christian sense to try to justify murder to limit murder. Long ago, Gandhi warned us what happens when we try to have the end justify the means-the means becomes an end. Let us attend to God's revelation: "Do not be conquered by evil, but conquer evil with good" (Romans 12:21).
Comparisons with Nazi Germany and Dr. Mengele do not enlighten but distract us here. The United States of America today is not Nazi Germany. We are a nation of law, even if not all our laws are just ones (e.g., legal abortion). We do elect our Legislators and Chief Executive: they appoint our Federal Judiciary. Christians (and all other citizens) are free to participate in that process-and they should participate actively and intelligently.
No Christian, however well-intentioned, has the moral right to declare himself the sole detective, district attorney, judge, jury, and supreme court in our democratic society and on his own authority set aside the natural law and the Ten Commandments, allegedly to advance the fifth of those Ten Commandments. For the first three hundred years of Christian history, the Christians were on the wrong side of unjust laws. Yet, they were convinced and taught us that it is better to suffer evil than to cause evil. "Know this, my dear brothers, . . . the wrath of man does not accomplish the righteousness of God" (James 1:19-20). That was infallibly true when written and is just as true today.
Legitimate defense
2263 The legitimate defense of persons and societies is not an exception to the prohibition against the murder of the innocent that constitutes intentional killing. "The act of self-defense can have a double effect: the preservation of one's own life; and the killing of the aggressor.... The one is intended, the other is not."
2264 Love toward oneself remains a fundamental principle of morality. Therefore it is legitimate to insist on respect for one's own right to life. Someone who defends his life is not guilty of murder even if he is forced to deal his aggressor a lethal blow:
If a man in self-defense uses more than necessary violence, it will be unlawful: whereas if he repels force with moderation, his defense will be lawful.... Nor is it necessary for salvation that a man omit the act of moderate self-defense to avoid killing the other man, since one is bound to take more care of one's own life than of another's.
2265 Legitimate defense can be not only a right but a grave duty for one who is responsible for the lives of others. The defense of the common good requires that an unjust aggressor be rendered unable to cause harm. For this reason, those who legitimately hold authority also have the right to use arms to repel aggressors against the civil community entrusted to their responsibility.