I'm going to split out some terms here. Scientific Method, Academic Science, and Secularism. The latter two are connected to atheism, at least in this era, and are more in line with ideologies and I do not desire to further address or describe them in this post except to say that they do not have a monopoly on the merits of the scientific method.
To speak of the method itself, which is religion agnostic and, as you say, it is a function to provide information as well as the ability to duplicate results. I would append that applying the scientific method to religion works, and that you can, indeed, learn as well as duplicate results through it - as well as reject results that do not work.
A major challenge is that the resultant artifacts aren't readily transferable or inspectable. Many secularists get hung up on this and say it's an invalid application. Essentially that only what the eye can see or the hand can measure is real. I can't really show you my happiness, or peace, or share with you the the depth of experience or knowledge that heals and transforms. I can tell you about it, about how Christ can lead you to peace. I can describe the inputs and results, the complete formula, and then you can walk it and experience the fruits first hand.
Another part of the challenge is that lack of transferability also applies to the instrumentation. I can't provide you a properly calibrated conscience, or the concept of true humility before God like I could a measure of mass or distance. It's all internal to you. Experimentation on that is time consuming and difficult. Some people run experiments with improperly calibrated instrumentation and then fail to get the expected results.
Because it was not about result. Or rather, it's never about the result. It's about the process, in same vain of procedural justice. It's about finding the provability.
The thing is if you can't move past that you have to make a result. Or the extreme, result is ignoble. That the process of proving the utmost important part. You will never get what scientific method is about. Just like your last paragraph. Sure, there are so many theories. Maybe even someone claimed that that harry porter is real! But why do you have to believe or not to believe if you only care about the process of proving and provability.
It's not about proving that the religious people are wrong(or proving irreligious people are wrong). It's about the fact that, for some people , they truly don't care about the result or take the result itself so far as undetermined (still care about the proving process though) and moved past it.
In general, cult of personalities are clearly examples of secular religion although one that can become supernatural in the case of the Kim dynasty in North Korea.
Ceremonies and traditions that we continue because 'that is just how it has always been done'. There isn't some binary notion of you are religious or your rationalist, non religious people can hold non-rationalist thought.
Personally I don't really understand what you're on about with the scientific method, the parent didn't mention anything on it.
Because there is a clean distinction between athism(not relying on belief) and antithesim. Scientific method is a lens of analysis tool and it's beyond the framing of belief as how religious people claims, or even how antithesim people claims. Just like how I would explain the same to the some antithesim group that science doesn't prove the god don't exist. That's still a misuse of the tool of scientific method. To believe the opposite is still a belief, and missing the mark of the scientific method where the most important part is the process not the result.
And that's where so called 'atheism is just a religion' got it wrong. No, it's not about getting a result. Scientific method is a way of processing information. It's about the process, not the result. It's not about believe the god exist or not(the result). It's about find out a way to prove (process). And it's perfectly fine if u can't produce a solid proof(provability). 'I don't know' is perfectly fine. You don't even have to believe, use the scientific method to analyze, do you best to deduce, and move on to the next topic. 'Religion' is just a topic to study. If people can't really grasp how scientific method and critical thinking works, they would never move past 'to believe' or 'not to believe'.