One reasoning Shia Muslims have given for disbelievers being najis is surah al-Ma'idah ayah 5:
"Today, all good things have been made lawful to you. The food of the People of the Book is lawful to you, and your food is lawful to them. The chaste believing women and the chaste women of the people who were given the Book before you, are lawful to you, provided that you give them their dowers, and marry them, neither committing fornication nor taking them as mistresses. The deeds of anyone who rejects the faith will come to nothing, and in the Hereafter he will be among the losers."
It doesn't say that the food of other people is lawful. But this reasoning is poor taking into account the context. The preceding ayat speaks about what is not lawful. This one speaks about what is lawful. Farther more the preceding verse 5:4 reads:
"If they ask you what has been made lawful for them, say, All good things have been made lawful for you; and what you have taught your birds and beasts of prey to catch, training them as God has taught you. So eat what they catch for you, but first pronounce God's name over it. Fear God, for God is swift in taking account."
Because the people were used to asking what is permitted, but are encouraged to ask instead what is prohibited, because as a rule the things that aren't prohibited are permitted.