But you see, when it doesn't support their narrative religious folk can just claim that the offenders are not real [insert religious group]s
Yes it's clearly 10x easier to oppress people when you maintain theocracy because you have complete control over the minds of people. However, the same thing can be done without religion.
All you need is a group of people to hate and enough people to hate them. After that you've essentially seized the power. Make any mistake politically and you can pull the 'x group is at fault' card and completely reflect any responsibility.
Hell if i wanted I could create an entire campaign around how people with dimples are the devil incarnate and should be pushed out of society. Anybody who doesn't have dimples and isn't smart enough to think for themselves will let themselves be spoonfed all the hate, and since they have something to agree on with me they gain my trust. Next step is the dimple holocaust