I seriously doubt if they would be offended; in fact, they might be honored to be invited into an American home. The Bible says, "Share with the Lord's people who are in need. Practice hospitality" (Romans 12:13).
At the same time, ask God to help you to be sensitive to them and their customs. For example, if their religion forbids the eating of certain foods, you'll want to avoid offending them. When you do invite them, explain that Christmas is a special holiday in our society, and you would be honored to have them share Christmas dinner with you and your family. If you're inviting others, let them know this so they won't feel awkward or surprised. Do your best, in other words, to make them feel comfortable.
If they do come, ask God to give you an opportunity to explain why Christmas is important to you. Remember: They may not even know what Christmas celebrates: the coming of Jesus Christ into the world. At Christmas we remember that God came down from heaven in the person of Jesus. As the Bible says, "The Word became flesh and made his dwelling among us" (John 1:14).
Whether they accept your invitation or not, take this as an opportunity to begin building a bridge of friendship with them. In other words, make it the first step in your relationship by reaching out and letting them know you care. God has put them (and thousands like them) in our midst; will we befriend them and share Christ's love with them?