The emperor Claudius had ejected "the Jews" from Rome for "fighting" over "Chrestus". Even in Paul's day, there was tension. Clement alluded to "jealousies" at the time of Peter and Paul, that led to their deaths.
Throughout the first half of the second century, the Roman church was led by a network of presbyters in a network of house churches, and these presbyters fought among themselves as to who was greatest. I've quoted Hermas from "The Shepherd of Hermas as saying, "They had a certain jealousy of one another over questions of preeminence and about some kind of distinction. But they are all fools to be jealous of one another regarding preeminence.”
This fighting continued on and on.
"In 235, two rival bishops of Rome, Pontianus (230-235) and Hippolytus (c.217-235) were exiled from the city by the emperor Maximin 1 because of street fighting between their followers." (Roger Collins, "Keepers of the Keys of the Kingdom," pg. 25)
"Because of the house-church system, such rival bishops could co-exist for as long as they had the backing of some of the city's many Christian groups. But the divisions usually resulted in violent clashes between the partisans of the two claimants, and in all cases the imperial government intervened to end the bloodshed and to send one or both of the rivals into exile, as happened in 235, and would do so again in 306/7 and 308." (Collins 26)
Note that in 150 they were fighting, and in 235 they were fighting, and in 306-308 they were still fighting. See a pattern? These last two incidents mentioned were during the fierce period of persecution known as "the Great Persecution," brought on by the emperor Diocletian and continued under his successors, until Constantine.
The pattern continued; as I mentioned, Damasus, "a man of much practical shrewdness and self-assertive energy" (Shotwell and Loomis, pg 595), became pope as his followers "launched an assault on the Julian basilica, seizing control of it after three days of streetfighting. When the backers of Ursinus (Damasus's opponent) occupied the Liberian basilica, it too was stormed. In the aftermath of the fighting, a neutral contemporary reported that the bodies of 137 men and women were found in the church." Collins 52). This last datum was originally reported by Owen Chadwick, "Catholicism and History: The Opening of the Vatican Archives, Cambridge 1978, pgs 110-116.
This is one reason, Matthew Bellisario, why your 19th century historians are not likely to have the whole story of the early papacy.
I doubt that we have it now, but we know more today than "the faithful" did in the 19th century.