Question: "Is it possible for someone to be pro-life and pro-choice?"
We should define our terms here. By "pro-life," we mean that we oppose the shedding of innocent blood, at any stage of development, including unborn children. If someone is "pro-choice" they mean that they believe it should be up to the mother to decide whether or not she will have an abortion, for any reason. If someone says that they are pro-life and pro-choice, this can only mean that they personally oppose abortion, but they think that others should be free to decide the matter for themselves, because they don't want to "impose their morality" on anyone else.
Is this a morally defensible position? To answer this question, we first have to ask why a Christian would oppose abortion? We oppose abortion not because we don't like it. We oppose abortion because we believe that it is the murder of an innocent life -- the only exception being the very rare circumstances in which it is necessary to save the life of the mother, and in such cases it almost always would mean the death of both mother and child to do nothing.
The Scriptures are abundantly clear that God takes the shedding of innocent blood very seriously. We are told that God destroyed the kingdom of Judah because they engaged in child sacrifice:
"And he [Manasseh] made his son pass through the fire [a form of child sacrifice], and observed times, and used enchantments, and dealt with familiar spirits and wizards: he wrought much wickedness in the sight of the Lord, to provoke him to anger" (2 Kings 21:6).
"Surely at the commandment of the Lord this [the destruction of Judah by the Babylonians] came upon Judah, to remove them from His sight because of the sins of Manasseh, according to all that he had done, 4 and also because of the innocent blood that he had shed; for he had filled Jerusalem with innocent blood, which the Lord would not pardon" (2 Kings 24:3-4).
The belief that abortion is murder is not a recently adopted Christian position. In the Didache, which is the oldest Christian document outside of the New Testament, it says unambiguously:
"Thou shalt not murder a child by abortion nor kill them when born" (Didache 2:2).
Canon 91 of the Sixth Ecumenical Council says:
"As for women who furnish drugs for the purpose of procuring abortion, and those who take fetus-killing poisons, they are made subject to the penalty prescribed for murderers."
Likewise, St. Basil says in his second canon:
"A woman that aborts deliberately is liable to trial as a murderess."
So an Orthodox Christian that actually believes what the Church teaches can only oppose abortion on the grounds that it is the wrongful taking of an innocent human life.
So can a person really be opposed to rape, but not want to "impose their morality" on others? No.
Could a person oppose lynching, but not want to "impose their morality" on others? No.
Can a person oppose abortion, but not want to "impose their morality" on others? No.
And as a matter of fact every law reflects someone's morality. There is no reason why Christians should not use their power to vote to influence the laws to protect innocent life.
One might add a quote or two to the scriptural references, e.g., Jeremiah's "The word of the Lord came to me saying, 'Before I formed you in the womb I knew you.'" (Jeremiah 1:4-5.) Also, David's prayer in Psalms 139:14: For You created my inmost being; you knit me together in my mother's womb."