Assuming Christianity is Avodah Zarah (RamBam), can one get his car fixed by a gentile, with a new part, put in, over Christmas? Obviously, there's no way to know whether the mechanic will work on the car on Christmas itself.
This in regards to Mishneh Torah Avodas Kochavim 9:1:
It is forbidden to purchase or sell any durable entity to an idolater within three days of one of their holidays.… When does the above apply? In Eretz Yisrael. In other lands, however, it is forbidden [to engage in such activities] only on the day of their festival itself.