Praise be to Allaah.
Relationships between people are of different kinds. If the Muslim has a relationship of friendship, love and brotherhood with a kaafir, this is haraam and may be kufr. Allaah says (interpretation of the meaning):
“You (O Muhammad) will not find any people who believe in Allaah and the Last Day, making friendship with those who oppose Allaah and His Messenger (Muhammad), even though they were their fathers or their sons or their brothers or their kindred (people). For such He has written Faith in their hearts, and strengthened them with Rooh (proofs, light and true guidance) from Himself. And He will admit them to Gardens (Paradise) under which rivers flow, to dwell therein (forever). Allaah is pleased with them, and they with Him. They are the party of Allaah. Verily, it is the party of Allaah that will be the successful” [al-Mujaadilah 58:22]
And there are other aayaat and ahaadeeth which convey the same meaning.
If it is a relationship based on selling or buying, or accepting an invitation to eat halaal food, or accepting a gift of something that is permissible, for example, without that having an influence on the Muslim, then this is permitted and it is permissible to eat the food offered by a kaafir to a Muslim if the food and drink are halaal. Even if it is presented in a vessel which has previously been used for drinking wine or eating pork, etc., it is still permissible to take it, so long as the vessel has been washed after being used for haraam or naajis (impure) things and all traces of them have been completely removed. If this will help to convey the message of Islam, this is a stronger reason why these invitations should be accepted and these relationships upheld, and there is more hope that there will be a reward in this case.