Would be more believable if they were fighting for believing in different gods.

That’s the difference in mentality for the fight to the death

Theist -> I wanna kill you because you are a threat to my beliefs but I’m willing to die because I believe there is an afterlife waiting for me.

Atheist -> I want to defend and preserve my life from your psychopathic beliefs because I believe there is no afterlife and this is the only life I’ll ever know.