Is there a contradiction between the prohibition of initiating greetings of peace with the People of the Book and the permissibility of consuming their food?

There is no contradiction between the prohibition of initiating greetings with the People of the Book and the permissibility of consuming their food. Their food refers to their slaughtered animals, which is a facilitation for Muslims, whereas we are prohibited from initiating greetings with them because there is no need or necessity for it.