It does nothing of the sort.
Rodney Stark uses all the original sources that were available to show there was a significant difference in how Christians treated others vs the Pagans around them.
It is a matter of percentages. Christian doctrine to love your neighbor as yourself, the example of the good Samaritan, and the exhortation to "love your enemies" are all unusual.
Stoic Philosophers pushed for the brotherhood of man. There is a melding of Stoic and Christian doctrine.
There is no question, however, that Christians taught their adherents to care for and value those outside of Christianity.
That was a very unusual concept in pagan Rome.
It does nothing of the sort.
Since it is exactly what you said, of course it does.
Plagues with massive rates of mortality are rare. In ancient times, and until just the past few hundred years, no one had any real idea about methods of transmissions, and obviously no access to the kinds of modern medicines and vaccinations which we know work.
Caring for someone had very little, if any, impact on mortality, other than exposing the caregiver to the contagions. People did care for one another anyway, and did so even when the only known Europeans were Neandertals.