I don't understand how this argues against religious totalitarianism.

Of course totalitarians will persecute and demonize anything that is a threat to their power, whether it's based in religion, ethnicity, or whatever else.

But if you already have a power structure there in the form of religion, and you rise through that, how will that do anything but aid your totalitarian efforts?

The existence of religious cults demonstrate that the religious affinity alone is insufficient to provide protection against arbitrarily nonsensical views (Heaven's Gate being an example of something that even makes political totalitarianism look tame). We have multiple examples right now of religion being used as part of an authoritarian-to-totalitarian approach (Saudi Arabia, Iran, Afghanistan, anywhere ISIS controlled).

If you look at the most authoritarian-leaning U.S. politician in modern times--Trump--you find that a huge fraction of his support is from those who claim to be religious. If you look farther back (e.g. to McCarthy) you see the same thing. Germany was pretty strongly Christian when Hitler took over--and neither the Protestant nor the Catholic churches put up much of a fight, with many Protestants especially viewing Naziism a welcome strengthening of nationalism. Only later did they have some misgivings, and as with any group that has misgivings and speaks out, they suffered in proportion to their opposition. Mussolini did not persecute the largest and by far the most powerful religion in Italy--Catholicism. He instead established an (uneasy) alliance.

I haven't read Arendt, but the thesis you're presenting just doesn't pass a basic examination.

In one particular scenario, where the totalitarian comes through a non-religious background (e.g. Lenin), organized religion provides a potentially potent adversary. But this is just one scenario. The modern examples of totalitarian-leaning regimes contain multiple ones with strong religious aspects (as well as counterexamples like North Korea).

Again, that a robust separation of power is protective is pretty obvious. The legislative branch, judicial branch, local government, journalism, religion, even education in the form of universities all have a role to play in resisting tyranny (presumably through the executive branch of any government).

But that people who are religious are plenty swayed by popular opinion and "expert" opinion (just religious experts), and people who aren't often have plenty strong foundational beliefs. I agree that populists take best advantage of weak beliefs, but there are many routes to developing a robust belief system, with religion being only one.

So I really don't see it at all. It seems to me like a self-serving rationalization by the religious as to why they're clearly on the right side (ignoring that in history they really weren't particularly). For instance, the strongest opponents of the Nazis were not any religious group but...the (secular) communist party (with their own strong, if wrong, belief system)!