Would it be foolish to forgive a boyfriend who cheated under these cirstances..?

Sweetie, you don't need anyone's permission to forgive him, you answered all the questions yourself. If you believe he is sincere in your heart of hearts, and you are capable of truly forgiving him and not punishing him subtly, then go for it! Everyone makes mistakes. The important thing is that you are not being taken advantage of. In your whole life, you want to cultivate relationships that make you feel GOOD about yourself, and you will be fine. Good luck!!