Dear Diego:

Before going into the issue of whether or not Pope Callistus approved of abortion, the point must be made, that non-Catholics tend to misunderstand, is that the mere personal opinions of a Pope are merely his opinions. A Pope's opinion is not binding on the Church and does not represent official "Church teaching". Thus, even if a Pope was in favor of abortion, such opinion is not Church teaching.

Now, as to Pope Callistus (217-222).

What we know about Pope Callistus comes from Julius Africanus, Eusebius, the Liberian Catalogue, and his two of his enemies Tertullian and Hippolytus.

Callistus was a slave who was given charge of the community bank. When money came up missing Callistus fled, but was caught and punished. He was soon released in hopes that he could recover the money. In his attempt to locate and recovery the lost money he got into a brawl in the synagogue on the Sabbath. For this he was sentenced to hard labor in the mines of Sardina, which was a death sentence.

When Marcia, the mistress to Emperor Commodus, sought the release of all Christians in the mines of Sardina, Callistus was freed.  He was placed by Pope Victor I in Anzio to live on a monthly pension.  After the death of Victor, his successor Zephyrinus recalled Callistus to Rome and put him in charge of the first official Christian cemetery on the Appian Way.  He eventually was made the principal deacon and advisor to the pope.  After the death of Zephyrinus, Callistus was elected the fifteenth successor of the apostle Peter and the sixteenth pope.

Because of this background, Hippolytus, in a manner not unlike the sedevacantist of today, refused to accept Callistus as Pope.  Hippolytus has himself elected as a anti-pope.
It is Hippolytus who falsely accused Callistus that lead to the false claim that he approved of abortion. This claim is totally false.

Hippolytus was a rigorist who believed that certain sins were unforgivable, such as adultery, fornication, and murder. To accept accusations from such a man is hardly a good source.

Tertullian also hated Callistus’ for this and stated in De Pudicitia:  "I hear that an edict has been published by the High Priest, the bishop of bishops, which decrees that sins of adultery and fornication are to be forgiven after penance and absolution.  What an edict! No good will be ascribed to it."

In the early Church it was common for people to believe that sins could not be forgiven after baptism. This is the reason that many who believed in Christ decided to not be baptized until close to death.

Rather than proposed a doctrinal error, Callistus did just the opposite. He affirmed that all sins could be forgiven in the Sacrament of Penance and that all people could be restored to the fullness of the faith, even those who committed mortal sins.
[Source: Fr. John Pasquini, Th.D.; 1917 Catholic Encyclolpedia.]

Anti-Catholics, as they are want to do, choose to rely upon sources that support what they have already decided or that support their bigotry. They are willing to overlook the veracity of their sources not caring whether or not their sources are telling the truth.

Another historical source that gets purposely misinterpreted is that until the 17th Century it was commonly thought that the unborn baby was not given a soul until "quickening". This was the common view of the Saints as well. Saint Anselm of Canterbury (1033–1109) said that "no human intellect accepts the view that an infant has the rational soul from the moment of conception". St. Thomas Aquinas said, "This sin [abortion before ensoulment], although grave and to be reckoned among misdeeds and against nature...is something less than homicide... nor is such to be judged irregular unless one procures the abortion of an already formed fetus."

This view of "delayed ensoulment" lead to the idea that abortion before ensoulment, while still a grave sin, was not murder. It was only after ensoulment that abortion became murder. Anti-Catholics turn this into an approval of abortion up to the time of quickening.

The notion of a delayed ensoulment coming from Aristotle was abandoned by the 17th century in favor of the view that the soul was present from the moment of conception. The scientific proof in 1827 of the existence of the female ovum and in 1875 of the involvement of the union of a gamete from each parent in conception reduced speculation about a delayed substantial change (Jean-Yves Lacoste (editor), Encyclopedia of Christian Theology, vol. 1, p. 4).

Regardless of these views, the Church has always considered abortion to be an evil and a grave sin.

Again, anti-Catholics are happy to distort the facts, ignore certain facts, and invent issues that so not exist to support their bigotries.

A good summary of this issue is found in an excerpt of the Pro-Life Activist's Encyclopedia, published by American Life League, "Chapter 43 — Abortion and the Catholic Church" found in EWTN's library.

I hope this helps.

God Bless,
Bro. Ignatius Mary