That's was one of the question I always wonder.... If you are in an society, that say in this case that Inquisitors have the right to try people on the spot, do not need to hear the accused, do not need evidence, can pass judgment on the spot as a single sitting judge and without appeal, are you supposed to loyal-neutrally embrace this job because "that's the law"? The NPC in case is certainly a jerk, but he's obviously empowered to do that by the lawful ruler of the land... The designers obviously thought that when procedures are blatantly wrong, but legal, a LN character would follow them [I didn't get the feeling he was having a blast burning people at the stake, he was just doing his best to protect his country against the demonic threat, much like McCarthy acted against the communists, except demons are real

].
I acknowledge that you are responding from the perspective of the character and this may not necessarily reflect what you believe.
That being said, I don’t believe this successfully defends the character in question, Halruun, LN Inquisitor of Iomedae, goddess of justice, for a number of reasons.
First, I am not inclined to cut any slack to an
Inquisitor of Justice for murdering a priest of a good faith, without even trying to listen to his defense. Even if he were empowered as an Inquisitor to act, it’s not Justice to decide he’s guilty and ignore his attempt to defend himself.
Need more? As an Inquisitor, doesn’t Halruun have access to the Zone of Truth spell? This is as if McCarthy had access to a Communist-detector, didn’t use it, and still thought his actions were justified.
Second, the burning of non-evil witches was also taking place before the fall of Kenabres.
Third, “that’s the law” is not a defence when as one of the highest ranking people in Kenabres, and a representative of the goddess of Justice, you likely have the power to change the law.
Fourth, burning non-evil people at the stake, even if permitted under the law, is still extremely evil. At best, Halruun’s actions are lawful evil.
At of course, as an Inquisitor, Halruun’s actions reflect on Iomedae herself. So murdering good-aligned priests without a trial and burning witches is definitely a bad look on the LG goddess of justice.