The moral logic is impeccable. If you truly believe that a fetus has the same moral status as a baby, and that, as Republican politicians have said, Planned Parenthood is akin to Auschwitz, abortion is a holocaust, and abortion providers are murderers, then you have a moral imperative to stop them, by any means necessary.
Funny thing. Nobody, including the Pope, believed that until the late 19th Century. Abortion (and for that matter infanticide) were commonplace in the Biblical world, and that was just fine with the Bible. It ought to be a major embarrassment to Christian anti-abortionists that the Bible not only completely fails to condemn abortion, anywhere, Old Testament or New; but actually to the extent there is any relevant text at all it clearly does not regard a fetus as a person and on the contrary appears to support not only abortion but the murder of pregnant women under certain circumstances. Here is the Skeptic's Annotated Bible on abortion. A few good ‘uns:
The Bible places no value on fetuses or infants less than one month old.
And if it be from a month old even unto five years old, then thy estimation shall be of the male five shekels of silver, and for the female thy estimation shall be three shekels of silver. -- Leviticus 27:6
Fetuses and infants less than one month old are not considered persons.
Number the children of Levi after the house of their fathers, by their families: every male from a month old and upward shalt thou number them. And Moses numbered them according to the word of the LORD. -- Numbers 3:15-16
God sometimes approves of killing fetuses.
And Moses said unto them, Have ye saved all the women alive? ... Now therefore kill every male among the little ones, and kill every woman that hath known man by lying with him. -- Numbers 31:15-17
(Some of the non-virgin women must have been pregnant. They would have been killed along with their unborn fetuses.)
Give them, O LORD: what wilt thou give? give them a miscarrying womb and dry breasts. -- Hosea 9:14
Yea, though they bring forth, yet will I slay even the beloved fruit of their womb. -- Hosea 9:16
Samaria shall become desolate; for she hath rebelled against her God: they shall fall by the sword: their infants shall be dashed in pieces, and their women with child shall be ripped up. -- Hosea 13:16
God sometimes kills newborn babies to punish their parents.
Because by this deed thou hast given great occasion to the enemies of the LORD to blaspheme, the child also that is born unto thee shall surely die. -- 2 Samuel 12:14
God sometimes causes abortions by cursing unfaithful wives.
The priest shall say unto the woman, The LORD make thee a curse and an oath among thy people, when the LORD doth make thy thigh to rot, and thy belly to swell. And this water that causeth the curse shall go into thy bowels, to make thy belly to swell, and thy thigh to rot: And the woman shall say, Amen, amen. ...
And when he hath made her to drink the water, then it shall come to pass, that, if she be defiled, and have done trespass against her husband, that the water that causeth the curse shall enter into her, and become bitter, and her belly shall swell, and her thigh shall rot: and the woman shall be a curse among her people. And if the woman be not defiled, but be clean; then she shall be free, and shall conceive seed. -- Numbers 5:21-21, 27-28
God's law sometimes requires the execution (by burning to death) of pregnant women.
Tamar thy daughter in law hath played the harlot; and also, behold, she is with child by whoredom. And Judah said, Bring her forth, and let her be burnt. -- Genesis 38:24
So there you have it. The literal, inerrant word of God.