This 2.0 post contains additional reflections on this topic.
Interesting post at Chronicon, "Sol Invictus evidently not a precursor to Christmas", about the allegation that Christians "stole" or "borrowed" December 25th from paganism. His conclusions:
A feast to Sol Invictus (the Unconquered Sun) did occur on December 25, but the earliest evidence for it dates from the mid to late 4th century. There is no evidence that Emperor Aurelian established a Festival of Sol Invictus (or anyone or anything else) on December 25.
Saturnalia did not occur on December 25 and had nothing to do with the birth of any god or anyone else.
Egyptians apparently presented an infant as a representation of the newborn Sun on the winter solstice, but this evidence also dates from the fourth and fifth centuries.
Hippolytus in 202-211 AD set the date for the birth of Jesus on December 25, because he thought Jesus was conceived 9 months earlier on the Passover, the day in which he also thought the world was created (5500 years earlier), the Vernal Equinox March 25.
Clement of Alexandria (193-215 AD) quoted various anonymous sources about the birth of Jesus and roughly agrees with Hippolytus, claiming that Jesus was born in late fall to early winter. Clement’s sources clearly seem to believe that Jesus was conceived on the Passover and was born roughly 9 months later; in fact the only difference between them and Hippolytus is that they differed on when the Passover actually occurred.
Dr. Tighe has written about this before, as cited in this post at Orthocath. Orthocath cites a similar piece here.
Of course, even if it could be established that Christians had borrowed a pagan date, or various other pagan "elements", this would not entail Christianity is secretly pagan, nor that it is derivative, since the meaning of various "pagan" elements (e.g. wedding rings) in Christian use are distinctly Christian. The argument that Christianity is derivative because it has parallels with paganism is little more compelling than the claim that there's no authentic Christian discourse because it used verbs, nouns, and other parts of speech after pre-Christians had done so. Orthocath offers his own prefatory remarks in the same vein to yet another piece he cites about "pagan Christmas".