It's a mistake to process these ideas on the basis of trust. True, the religious angle is shoehorned at the end. But the author cites secular books and ideas throughout; these ideas and the relationships between them are worth considering.
Imagine that a person was trying to explain to you how we knew that galaxies and so on were a certain distance away. They show that we know how to figure out Standard Candles and luminosity etc etc etc. They also claim, at the very end, to say that the earth is flat. They don't mean the universe is flat. They mean the earth is flat.
Now, imagine you haven't read the article, somebody comments, "This guy said the earth is flat!" and you ctrl+f into the article and they did, in fact, write that. Should you be encouraged to read the article? They have some secular studies and ideas.
But they're not talking about something you cannot "verify" with your own mind right now, at worst with some additional reading. You're not asked to "trust" anyone.
"That person freaked out just because someone said the Earth is flat, so that their brain completely glazed over and they couldn't understand or care about anything else they said", why is that not a thing, too?
To me this kind of discussion is not intellectually honest, it's not an earnest attempt -- there's plenty brilliant people of faith so I see no reason to dismiss anything out of hand like that. Don't judge a book by its cover, yet this discussion about the cover is the one that the most energy is spent on.
It's possible to be right about the universe and the galaxy but wrong about the earth. The 90% that is accurate is still accurate even if another 10% is wrong.
More pointedly - we are all in the same position as the flat-earther you posit. None of us have 100% accurate knowledge - meaning some percentage of what we believe is either false or one day will be proven false. We all have blind spots. Flat earthers have a particularly egregious blind spot. So we can be skeptical of other claims they make. But we should still engage with the stuff that makes sense and coheres. The answer to bad science is more science; the answer to bad speech is more speech.
