I think this is another example, where very different levels of “belief” are treated as if they were identical.
The belief in any kind of god adds an element into your explanation that is purely fictional because there is no observational evidence for its reality.
And more, it’s easily identified as obsolete for an adequate explanation: If I want to explain what thunder is, I can observe the phenomenon with various means, make some tests to verify observations under controlled conditions and can then conclude that the phenomenon occurs, when the electricity of lightning hits the air and starts it vibrating, which – as I can test – produces a sound. I can also verify that the heat caused by lightning leads to an explosive expansion of the air, which adds another vibration. And so on.
Of course, I can include an element like Zeus in my explanation who I hypothesise is behind the phenomenon – but I can also add ad libitum Thor here or Indra or any other god who people believe(d) is responsible or a god I make up on the spot, like Brztlfazizl, causer of thunder, migraines and Mai Tais.
But what do I gain by such an addition? Can I produce thunder with a prayer to any of those gods? Or does it not occur when I deny their existence? Can I, in any way, find evidence that the element is needed for my explanation?
The answer is “No”, invariably “no”.
And since it is no, there is no reason to include it in my explanation.
Does this mean I don’t need any belief at all in the existence of the natural elements I included in my explanation or the rules that I modeled to guide their interactions?
Well, no. I do need such a belief. But that belief can be easily verified by the observations and experiments by other people. Reproduction of results is the key here.
If you can produce specific results by believing in a Brztlfazizl, that new element will be tested by other researchers and if they verify your results, we will drink a lot more Mai Tais in the future.