May one give a present to a gentile in honor of his Holiday, such as X-mas and New Years?
It is forbidden to give presents to an idol worshiper [even if he is an acquaintance] on the day of his Holiday. If however the gentile does not believe in the idol and does not worship it, then it is permitted to do so. Christians, who believe in the deity of a human and worship him, are considered to be practicing idolatry, and it is therefore forbidden to give them presents on the day of their Holiday, which includes Xmas and New Years. Nevertheless, some Poskim rule that the above prohibition only applied in previous times when people were much more religiously observant of idolatry, however today the worshippers are no longer expert in idolatry, and it is therefore permitted to do business with them on the day of their holiday [and give them presents, if they are an acquaintance]. This especially applies if segregating ourselves from the gentiles on the day of their Holiday will bring enmity and hatred towards us, being we live amongst them and have business relationships with them throughout the year. Nevertheless, a Baal Nefesh is to distance himself from rejoicing with them if he is able to do so inconspicuously, in a way that will not arouse enmity. Thus, practically, if one needs to send gifts to a gentile [acquaintance] on the day of their Holiday, such as New Years [or Xmas], it is permitted to do so. However, if possible, the present should be sent before the Holiday begins, such as the afternoon prior to the Holiday. If this is not possible, then the gift may be sent on the Holiday itself.
 Michaber 148/5; Avoda Zara 65a
 Rambam Macalos Assuros 11/7; Avoda Zara 9/4; Pirush Hamishnayos Avoda Zara 1/3; Rama 148/12 [in uncensored editions] lists Xmas and New Years as Holidays of idolatry. Rebbe in handwritten editing remarks to a letter “Christianity is Avoda Zara, is in contrast to the seven Nohadite laws, as opposed to Islam. However the Christians of today are simply “Maaseh Avoseihem Beyadeihem”.
 Rama 149/12 [in uncensored editions]; Terumos Hadeshen 195
 Opinion in Michaber 148/12; Tur in name of Rashbam; Tosafus
 Michaber ibid
 Rama 149/12 [in uncensored editions]; Darkei Moshe Haaruch 148/5; Terumos Hadeshen 195
 Rama 149/12]; Terumos Hadeshen 195