You have a couple of different questions, here.
The first question is can a person be rejected as Christian for holding a pro-choice position?
The answer for the overwhelming majority of mainstrean Christain denominations is “No.” There is a fairly small subset of Christian denominations (with Jack Chick at the extreme end) who hold that anyone who does not believe exactly what they believe is not a Christian or is not “really” a Christian. The more mainstream position would be that the person who holds a position contrary to a particular Christian doctrine, but who has been Baptized, is a Christian. The person may be viewed as wrong-headed, heretical, or sinful, but that does not make them stop being Christian.
Considering the issue of one being “pro-choice,” the issue would not even have arisen prior to the 20th century. The majority of Christian denominations followed existing belief from the original positions of the Catholics and Orthodox (since abortion was not really a matter on which the Reformers differed from the RCC). It was not until fairly recently that anyone in civil society (in Christian dominant countries) ever argued a “pro-choice” position, so there was no reason for the churches to tackle the issue of a person who promoted a pro-choice perspective.
A general history of the Catholic tradition can be found in the early 20th century Catholic Encyclopedia. The current views of the RCC can be found in the Catechism, sections 2270 through 2275.
The attitudes of the RCC toward pro-choice persons would not require a specific statement. It is a general approach to any issue that a person who publicly challenges the teachings of the Church is acting against the church, that is, being a heretic. A person who believed a pro-choice position, but who never publicly declared that position would generally not come under church scrutiny, althoug if someone made an issue about such persons, the church would probably assert that they were being heretical.