We do not, and cannot, know how much of the Roman population was Christian at a given time. Although Early Christian literary sources sometimes count the converted in a given city, these numbers are impressionistic and rhetorical. Archaeology , likewise, sometimes uncovers Christian meeting places and artifacts; but these provide nothing more than a snapshot of a given community in a given time. So we are reduced to modeling.

Prof. Freedman's source is probably Rodney Stark's Rise of Christianity, which estimates (pp. 6-7) that Christian numbers grew by 40% each decade from the first century onward. Assuming that about 10% of the Empire's population was Christian in 300 (more on that in a moment), this growth rate would create a Christian majority (56% of the population) by 350. Stark was modeling on a purely speculative basis, trying to find a growth rate (arbitrarily assumed to be more or less constant) that would fit the rapid rise in Christian numbers that must have occurred in the early centuries of the Church. We have no way of proving or disproving such a growth rate; but there is reason to suspect that the conversion of the Empire was a more gradual process than Stark's modeling might suggest.

Most scholars assume, as mentioned, that about 10% of the Roman Empire's population was Christian in 300 CE, on the cusp of the Great Persecution. This estimate is ultimately founded on Adolf von Harnack's Die Mission und Ausbreitung des Christentums, which assembled all the evidence available in patristic and Roman sources, and finally suggested - as a sort of scholarly guesstimate - that the number of Christians in the Empire may have grown to 10% of the population (roughly 6 million) by the turn of the fourth century. The great majority of these Christians lived in the Greek-speaking eastern provinces (Harnack though that as many as half the inhabitants of Asia Minor (modern Turkey) may have been Christian by 300), with additional clusters in and around a few western cities (notably Rome itself) and parts of North Africa. It is generally assumed that there were very few Christians in the northwestern provinces, particularly in rural areas.

Most of the growth in Christian numbers must have occurred in the third century. In his article on "Christian Number and its Implications," Keith Hopkins - like Stark, postulating a steady growth rate from the first through third centuries - suggests an increase from something like 200,000 in the year 200 to about 6,000,000 a century later. And we have no reason to doubt that steady growth continued through the fourth century, particularly after Constantine's conversion made a hitherto illegal cult into a state-sponsored religion, and Christianity vaulted into intellectual and social respectability.

I would hesitate, however, to assume that half the Roman world was Christian by the middle of the fourth century, or that virtually had been converted by the century's end. That a phenomenal increase in Christian numbers did occur is impossible to doubt; but no matter how numerous and zealous the missionaries, the overwhelmingly rural nature of the Roman world would have militated against such exponential growth.

The Roman Empire had about 2,000 cities, most quite small, the majority concentrated along the coasts and major transportation arteries. Together, these cities may have housed, at most, 15% of the Empire's population. The rest lived in tens of thousands of widely-dispersed villages and farmsteads. Christianity does seem to have been widespread in the rural districts of some provinces by the beginning of the fourth century. Even in the reign of Trajan, Pliny had noted Christians living in the countryside, and there is evidence for very considerable rural communities in third-century Tunisia, Egypt, and Asia Minor. It is equally clear, however, that the rural populations of most provinces remained largely pagan for a long time. It is telling that "pagan," which began as a Christian term of abuse for the stubbornly polytheistic, literally means "hick." As late as the mid-sixth century, John of Ephesus could covert 80,000 rural pagans on a single, very busy missionary trip - and this in Asia Minor, probably the most heavily-Christianized part of the Empire.

Prof. Freedman (and Rodney Stark) may be broadly right in their estimates. But there is reason to believe that Christians were a minority, at least in parts of the Empire, through the fourth century.

/u/toldinstone has mentioned Stark and Hopkins, however, we can go back a lot earlier to find this sanguinity about the penetration of Christianity throughout the empire.

Tertullian in roughly 211, suggests in Adversus Scapulam that Christians were 'pars paene maior civitatis cuiusque' - 'almost a majority, everywhere', which is a good century before 300, and while some have taken it to be gospel closer to our times, it is dismissed, rightly as being far too generous.

Harnack^1 mentions John Chrysostom's mention of half the city being Christian during Theodosius I's reign, and which he upgrades in a letter to Theodosius II in 423 (CT 16.10.22), to the point that there are virtually no non-Christians left (although as MacMullen points out, this is an offhand remark, not a statistical estimation). Augustine also notes the Christian population constitutes the 'whole globe' (Sermon 62.4).

It might also be Stark as mentioned elsewhere. He has a 40% growth rate, which he finds confirmation in the rise of Mormonism, but his conclusions and his statistics are challenged. There are noted problems with Stark's thesis (and others), as Thomas Robinson laid out in 'Who were the First Christians? Dismantling the Urban Thesis'. First, is Stark's suggestion that students should ignore their historian professors who don't like Stark (!):

Many historians, especially those devoted to ancient history, will receive this book with the deepest of suspicions; and others of them, with enthusiastic contempt. Of course, I didn’t write it for them. I wrote it for the general reader, for numerate scholars, and especially for graduate students in history, to tempt the latter to pursue more disciplined and sophisticated undertakings. Cities of God, p.213

There are other issues with Stark not checking his sources properly or getting facts wrong, but the general savagery of Robinson's commentary on Stark is worth checking out. To Robinson, Stark has been provocative, but hasn't hasn't done anything more than add a veneer of (false) mathematical respectability to the 10% thesis of Harnack. Robinson suggests stopping estimating raw numbers at all - there's too little data to build anything coherent on it.

^1 Harnack is really the ur-guesstimator, as almost everyone else guesstimates the same as he did - MacMullen, Lane Fox, Stark, Drake, and Harnack all hover around an estimation of between 4-12% by the 3rd century.

I suppose I have a follow-up question, in general, would undergraduate survey course lectures, particularly from a non-specialist in the field, absent any other sources, be considered a reliable source, either to cite on this site or a research paper, or just in general?