Praise be to Allah.
It was reported in the hadeeth that you should say salaam to those you know and those you do not(narrated by al-Bukhaari, 12; al-Fath 1/55) but this applies only to Muslims, or those who appear to be Muslim. It was also reported that it is forbidden to say salaam to Jews and Christians, because the Prophet (peace and blessings of Allaah be upon him) said: “Do not initiate the greeting of salaam to a Jew or Christian, and if you meet them in the street, push them to the narrowest part of the road.” (Narrated by Muslim, 2167). He also said: “If the People of the Book greet you with salaam, say ‘wa ‘alaykum’ (and also upon you).” (Narrated by al-Bukhaari, 6258).
But at that time the People of the Book were distinct from the Muslims in their dress and appearance, and they were not allowed to resemble Muslims. But in these times, unfortunately, many Muslims look like them, and we can no longer tell the difference between a Muslim and a Christian. Everyone - except for those whom Allaah wills – looks the same in dress, in being clean-shaven, in wearing nothing on their heads, or wearing western-style caps, so the matter is more confusing. If someone who looks like the mushrikeen says salaam to you, say “Wa ‘alaykum,” and do not initiate the greeting, because of the uncertainty about him. If he objects and tells you off, then apologize to him. You had reason to act as you did, because you did know whether he was a Muslim or a Christian, because he is not dressing as a Muslim and prefers the dress of the Christians and others. Tell him that “whoever imitates a people is one of them”(Saheeh, narrated by Imaam Ahmad, 2/50-92), and advise him to distinguish himself from the kuffaar and to dress as the Muslims dress, like his father, grandfathers and the scholars of the Muslims. If he persists in what he is doing, this means that he likes the characteristics of the Christians and is imitating them, and that he despises the Muslims and is going against them, even though he does not gain anything from that besides blind imitation. This indicates that he admires those kuffaar and thinks that their worldly achievements and inventions, etc., stem from their false religion. This is going too far, for the Muslims are wiser and more able to invent and produce, so he should not be deceived by the Mushrikeen.