Option 1) All the flipping Jews were traveling at the same time because of extraordinary circumstances. Also, the fact that xmas is chock full of northern European paganism (yule logs, adorning trees, mistletoe, gift-giving in late december, etc) is a coincidence.
Option 2) Jesus was born in the Spring or Fall, when all the Jews would be traveling for their normal religious observances.
Option 1 requires a boatload of unlikely assumptions. Option 2 requires literally none. Occam's Razor dictates Option 2.
The fullness of evidence, including Church tradition passed down from the Apostles who knew Christ and the Blessed Mother directly, tilts the balance in favor of Option 1.
The pagan elements "baptized" into Church tradition w.r.t. Christmas is not the same as the basic facts about Christ's birth themselves.
Mark 7 would like a word with you about "Church tradition".
Mark 7 does not condemn tradition. It condemns any tradition that deviates from charity and the will of God. Christ did not condemn the Pharisees for holding the Old Law; Christ repeatedly encouraged people to stay faithful to the Law, without placing the Law above charity, since that is (part of) what it was there to preserve.
That Christians have done things a certain way in accordance with Scripture, and sufficient reason is required to deviate from those ways and interpretations, is not a bad thing and not to be condemned.
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