Answer
Since the followers of the past revealed religions (that is, the Jews, the Christians and the Zoroastrians) are ritually pure, many of the problems concerning the status and permissibility of the food are resolved when we live in their midst. It becomes permissible for us as Muslims to eat from their food no matter whether they touched it with their wet hands or not as long as we do not know or are not sure that it consists of what is forbidden to us, like intoxicating drinks. As for meat, fat and their extracts, they are Haram and cannot be used unless one is sure that they are Halal.