To be fair, Kane did specifically say they should try Finn for war crimes and implied that a conviction and death sentence would not just be expedient and merciful outcome, but also a correct one. Jaha also did make a case that they should turn Finn over but Abby was not in the head space to hear it (my theory is…

Abby is not a good leader and is not supposed to be. The fact that she selectively enforces the rules based on what works for her is supposed to be a failing, even if it is annoying.
Remember, the only reason Finn had a gun was that Abby and Bellamy stole it for him to find Clarke even after Kane and Major Byrne…