Apparently not. This guarded opinion-piece by a Muslim demonstrates as much by relying on a hadith — one, however, that is no where near as indicative as others. More telling hadiths report Muhammad saying:
“Do not greet the Jews and the Christians before they greet you and when you meet any one of them on the roads force him to go to the narrowest part of it” [Sahih Muslim B26N5389].
Sahih Bukhari relates Muhammad saying: If Jews and Christians say “Peace be upon you,” say only “And on you” — but do not add the word “peace,” which is always included in return greetings to fellow Muslims: “And peace on you” [Sahih Bukhari B26N538].
If simply wishing “peace” upon non-Muslims is problematic, need one ponder long whether or not Muslims should respond with “Merry Christmas” — a saying that implicitly acknowledges the divinity of Jesus, otherwise anathema to Islam — to infidel Christians?
Maybe Muslims can simply say “Happy Holidays”? A fatwa addressing this question — dealing specifically with whether “holidays” has pagan, mushrik, connotations — is certainly in order.
“Can Muslims say ‘Merry Christmas’?” by Mahmudi Asyari and Muizzudin for the Jakarta Post, December 24:
Indonesian Muslims still have very different opinions about wishing someone “Merry Christmas”. Some of them believe it is OK to do so, while some others see it differently.
The former group base their opinion on the spirit of religious tolerance and the latter group consider it harmful for the religion and relate their opinion with the forbidden action of mixing one religion with another. This group seems to be dominant in Indonesia.
If “this group” is “dominant” in Indonesia — for long, the one Muslim nation tauted as most “tolerant” and pluralistic” — what does this say about the average Muslim nation’s views on saying something as simple as “Merry Christmas”?
In defending their opinion, they use a hadith as mentioned in Bukhari: “It [is] related from *Aishah that a group of Jews came to God’s Messenger and said, ‘as-sam *alayk (death be on you). I understood it and said to them, as-sam wa al-la*nah (on you be death and curse).
God’s Messenger said, ‘Be calm! O *Aishah, for God loves that one should be kind and lenient in all matters.’ I said. ‘O God’s Messenger! Haven’t you heard what they have said?’ God’s Messenger said, ‘(Haven’t you heard what I have said.) I said (to them), *alaykum (upon you).'” According to them, responding to a greeting with non-Muslims is limited and so is wishing “Merry Christmas”…