Create More Date ContraversyControversy
There are several Christian churches today, particularly Church of Christ branches, that refuse to celebrate Christmas because it isn't biblical. They note that we do not know the date, so it is a falsehood to claim that as the date of Christ's birth.
Given that established pattern, you might be able to stall Christmas in its early years by painting the celebrants as unholy savages guilty of modifying God's Word. Certainly you could attack it during the Reformation and at least cut out the Protestants from celebrating it.
Your one major risk: a celebration in dark of winter is almost inevitable. You might stop Christmas, but I bet something replaces it. "It came without trees and without toys, it came without God or silver bell noise. It happened just from fear of the dark, so now we celebrate First Spark. Or something like that, because you see, Christmas is more than just Christianity!"
So maybe use your machine to cause something horrible to happen every solstice. Do that enough years, people will come to dread that time of the year.