I don’t think him him being Muslim had to do with the killing. He was obviously completely unprepared to be a police officer.
The woman was inappropriately dressed. She approached a man without a male relative escort. She thus pushed the Moslem’s buttons big time. He was totally uncomfortable in her presence and had to do something to change the situation. He is a Moslem so he killed her which in his mind is exactly what was necessary and what a father or brother would have done.