First of all, to give you some context, there are 3 characters that will be referred to as A, B, and C. The following lines are from a dialogue between A and B about C. The character C has done things that are considered wrong, unforgivable actually, and that's why in the dialogue there is 許される.
Character A does not approve of what C did. However, B is grateful; he is on the side of C.
I'm fairly certain that A is saying something like "But, it's unforgivable."
"That sort thing shouldn't be allowed." (referring to C's actions)
The subject are his actions, right? I say this because if A had wanted to say "I can't forgive/allow/him for what he does", I believe (あいつを）許せない would have worked or 許されない.
Regarding B's line where he says 許されるって誰に？ if it sounds like he doesn't approve of what A said, and given that he also quotes what he said (with the use of って), personally I consider that it would have sounded better if B had also negated the verb, as in, to say: "Unforgivable, you say? By whom?"
Would have made sense in my opinion and much easier to translate, but it's not like that and I'm not sure what B is implying.