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A Muslim can offer the greeting of peace to a group of Muslims and unbelievers providing that he intends it to Muslims. The Prophet used to offer peace greeting when he passed by a group of Muslims and idolaters.
Muslims are required to disown unbelievers for God’s sake without harming them. They just have to maintain good peaceful relationships. But taking non-Muslim as intimate associates is not permissible.
It is permissible to exchange visits with non-Muslims when necessary or if it will help Muslims to introduce Islam and giving some advice which is a noble purpose. The Prophet himself used to visit non-Muslims.
There are two views on offering unbelievers a greeting other than peace or starting with an ordinary greeting. One view permits offering a general greeting. The other forbids to start by greeting a non-Muslim
There are different views on greeting unbelievers. Some consider it accepted to start by offering the greeting as a way to win their goodwill. Others only allow Muslims to reply the greeting and not to start it.
It is perfectly permissible to offer gifts to unbelievers who are at peace with Muslims. But the permissibility excludes giving them gifts at their religious feats as this would be an approval for their unbelief.