If the Prophet wanted to eat when he was sexually impure, he would wash his hands.
Sunan Ibn Majah Book 1, Hadith 327
← Previous Hadith "The Prophet was asked about whether a person who is sexually impure can sleep, or eat, or drink. He said: 'yes, if he does ablution as for the prayer.'"

Sunan Ibn Majah Book 1, Hadith 326 Next Hadith → "I entered upon 'Ali bin Abu Talib and he said: 'The Messenger of Allah used to go to the lavatory and relieve himself, then come out, and he would eat bread and meat with us and recite Qur'an, nothing stopped him' or perhaps he said: 'prevented him from doing so except sexual impurity.'"

Sunan Ibn Majah Book 1, Hadith 328