Islam cares much for the relations between Muslims and non-Muslims. It makes it clear that Muslims, on meeting, should greet one another with “As-Salam `Alaykum”. In his hadith, the Prophet (peace and blessings be upon him) said: “Never will you enter Paradise until you are true believers. You will never be true believers until you show love to one another. Shall I inform you of something which, once you do it, will disseminate love amongst you, exchange ‘Salam’.”
Islam also shows that certain forms of greeting are to be avoided so as to keep the Muslim creed intact from shirk. But at the same time, Islam pays due respect to some fine traditions that do not collide with its teachings and are kept within bounds so as not to take any form of shirk.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
“As a Muslim you should greet people with the greeting of Islam, which is “peace”. You are allowed to greet anyone with this greeting of peace regardless of his religion, race, or ethnicity, for we are to wish peace to everyone who is not in a state of war with us. If a Hindu greets you with “namaste” you can greet him back with “namaste” provided you understand the meaning of the word and it is not contrary to the Islamic beliefs and practices. In other words, if the idea is contrary to tawheed (oneness of Allah), then we are not allowed to use it. If there is no such idea implied, then certainly we can return with the same greeting. I don’t think the above words have any such unsavory connotations or meanings. In other words, the meanings you have indicated are acceptable in Islam.
Islam teaches us that we are to wish good and peace to everyone, and if someone wishes us peace and goodwill we must reciprocate in a similar way or with a better greeting and not with something less. Allah says, “When you are greeted with a greeting, return it with a better greeting or its equal. Surely, Allah takes account of all things.” (An-Nisa’: 86)
But it is only fair as a Muslim to greet people using the greeting of Islam, which is the greeting of paradise. Let the Hindu or Sikh choose whatever greeting they choose to greet you with; you are not to impose yours on him.”