How can it be explained that the Prophet ate from the food of the Jews when their money is considered forbidden or reprehensible due to its mixing with unlawful earnings? And is it conceivable that the Prophet would commit an act that is reprehensible in Islamic law?

The Prophet, peace and blessings be upon him, eating from the food of the Jews was permissible. His action in doing so might have been for the purpose of legislating and clarifying that this act is not forbidden. This is what makes the act, for him, an act of proximity [to Allah], whereas it might be disliked for others. There is another opinion that considers eating from mixed wealth not disliked, and this view is considered to have a sounder argument.