“Therefore, to stop the rumor [that he had set Rome on fire], he [Emperor Nero] falsely charged with guilt, and punished with the most fearful tortures, the persons commonly called Christians, who were [generally] hated for their enormities. Christus, the founder of that name, was put to death as a criminal by Pontius Pilate, procurator of Judea, in the reign of Tiberius, but the pernicious superstition - repressed for a time, broke out yet again, not only through Judea, - where the mischief originated, but through the city of Rome also, whither all things horrible and disgraceful flow from all quarters, as to a common receptacle, and where they are encouraged. Accordingly first those were arrested who confessed they were Christians; next on their information, a vast multitude were convicted, not so much on the charge of burning the city, as of “hating the human race. In their very deaths they were made the subjects of sport: for they were covered with the hides of wild beasts, and worried to death by dogs, or nailed to crosses, or set fire to, and when the day waned, burned to serve for the evening lights. Nero offered his own garden players for the spectacle, and exhibited a Circensian game, indiscriminately mingling with the common people in the dress of a charioteer, or else standing in his chariot. For this cause a feeling of compassion arose towards the sufferers, though guilty and deserving of exemplary capital punishment, because they seemed not to be cut off for the public good, but were victims of the ferocity of one man.”
— Roman historian Tacitus’ account of Nero’s persecution of Christians, from his book Annals, published a few years after the event. At the time, Tacitus was a young man from an equestrian family (roughly equal to a knight’s family) living in Rome.
I’m guessing the charge of “hating the human race” was due to Christians’ refusal to participate in sacrifices to the gods. The gods would be angry at any part of a society refusing to pay homage, and if the gods are angry the whole community is punished. So, to pagan Romans, Christians lacked civic virtue and were putting them all in danger by refusing to honor their gods.
Accordingly, the test of whether or not someone was a Christian was essentially demanding they sacrifice to the gods. If they did, they were okay by the Romans and let go. If they refused, they were punished.
When Christianity became the religion of the Empire, one of the first controversies among Christians was whether or not to let the people who sacrificed to save their lives back in to the community of the Church.