Religion does not imply Theism / Theocracy
By paraphrasing the old expression "Correlation Does Not Imply Causation", I will simply say that you have no problem here because religion does not imply theism/theocracy.
Now granted in real life there is a strong connection between faith and doctrine because the religious institutions claim that the ethics and morals that are in their religious doctrine are valid for all people. But their only ground for claiming this is "Because our holy texts say that these ethics stem from the highest authority, i.e. the divine creature(s) to which we have pledged our faith". Without that, they have no basis for claiming that their doctrine should be universal.
So in your world, things do not have to be like in our real-life world, because you make no reference to having divine entities that claim ultimate authority to dictate doctrines. So whatever doctrine needs to be in place in order to not screw up the world Westeros- or Broken Earth-style is not at all related to ethics or morals. The fact that you need to perform a certain ritual in a specific way at a specific time, does not in any other way imply things like the ten commandments or the eight condiments.
In fact, one could argue that what you have here is not a religion at all. What you have is unexplored reality; physical science waiting to be performed. Unexplained does not mean mystic. And with a lack of mysticism, any measurable, explorable part of reality is just that: plain old unexplained reality, not religion.
Compare real life; we have no idea why gravity exists or what the fundamental causes of it are, but we none the less know how to deal with gravity because we know how it works because science has explored gravity and found out good models of gravity that fit the measurable reality.
In the same way, your fictional characters know how to deal with the threatening calamities in order to keep them at bay. They have no idea why they have to do it the way they do, but they know that if they do not, things become messy.
There is no problem here
...because your religious leaders do not claim ultimate authority over every aspect of life. They are experts in warding off calamities by knowing the rituals and being in tune with what the great unknown demands. But unless they claim ultimate authority over everything simply because they desire power, there is no issue here.
What about abuse?
Ah, what if the religious leaders decide to play dirty and start claiming they do have authority? That to me sounds like a great plot generator. Is this something for you as the author to be worried about, or to use as an endless well to pour from?
Since you can dial the religious leaders' ruthlessness and ambition back and forth as much as you like, and seeing that you can dial the people's skepticism back and forth as much as you like... you simply need adjusting these to whatever levels you need to create the right kind of discord needed to make a good setting/story.
Also let me point out that if the people of your world have never before had to endure deistic/theistic kinds of religions, then they are not at all used to the notion of cults where someone claims someone or something has ultimate authority over everything. If you set it up this way, the notion of an ultimate authority will be as alien to them as the cult of personality of Kim Il-Sung is alien to you and me.