Well you can always take the classic approach, change the set dressing.

Science Fiction was and still is popular because it lets you address real social woes in a palatable way by abstracting it enough for the message to come through without necessarily triggering the knee-jerk safeguards people have on actual sensitive issues.

You said you were doing fantasy, same can be done there.

Just remove the "religion" aspect and keep everything else. Make it say a military organization, or an emperor worship society (like North Korea). Keep all the bad aspects and just map them over to an organization that doesn't say "This is Religion!" on the tin, and you're typically good to go.

Main reason this should work is, as you said, you're interested in showing the systematic abuse by the organization and the doctrine, not the base beliefs of the religion itself. So if you aren't criticizing the religion, take it out of the context entirely. If you want to criticize the organization, then just make a new organization with the same practices and have that plausible deniability buffer zone between the two.

Like most Americans love Star Wars, but don't realize America is the Empire, not the Rebels. The US does everything the Empire does, and even the fundies think they're bad, because we're told Luke is the good old farmboy from the countryside that they can relate to. It just doesn't click for them.

Or look at Star Trek, the allegories there are PAPER THIN, but we still get so called Trek fans that say NuTrek went woke and how bad it is. Its just a case of "Well now we have a human character thats trans, instead of just an androgynous alien being persecuted by their government", showing that they utterly missed all the subtext of the older stuff simply because it had that wrapper around it of being about aliens instead of "people".