Hello again Marta,
Nice to see your curious questions, expressing willingness to hear a different viewpoint than Barrett’s about the subfield of “evolutionary psychology” (eVopsych).
“I’m not saying that you’re not right, but the opposite side is using exactly same argument when Christian scientists are saying pro religion stuff. So if both sides say the same thing, does the argument cancel itself out? Are both sides equally right? Or wrong?”
Could you please clarify, which are the “sides” involved here, and which do you consider yourself on? We’ve only had a couple of exchanges, and I don’t read here much these days. I don’t think “the argument cancels itself out”, though not exactly sure what you’re asking or “from where are you coming” with your ideas.
“What do you mean blind and neutral? As in neutral about religion? I can’t see how anyone in reality can be that… Those who claim they are, are usually agnostics leaning towards atheism, how is this neutral?”
No, not neutral about religion. I agree with you about “usually agnostics” or “leaning towards atheism”, and more likely already atheists, are the VAST majority, almost the exclusive realm of people working in eVopsych. Barrett is an outlier here, quite clearly, though it’s not obvious to me that anyone here knows why that is. I’d be pleased to hear someone linked to BioLogos explain why they think that is, i.e. address the “sociology of eVopsych” as a subfield within psychology. While I’m not a psychologist myself, I’ve done research on eVopsych and have published a few texts, including sections from one of my two books, which directly addressed eVopsych in one chapter. Justin Barrett was not on my radar then, though I doubt I’d have used his “curious” work anyway.
Regarding the quote you found re: “to find belief in divinity quite natural”, let us confirm that “strictly natural” differs from “quite natural”. Do you agree?
To say, “It’s quite natural to be religious” isn’t all that controversial. Yet, “religion” isn’t a “strictly natural” phenomenon. Do you disagree?
“the Idea that we are evolutionary likely to believe in God can’t be this bad”
This is a fine line, and depends on the person’s worldview. Not knowing yours, it’s hard to say. There are many people who distort theology with “evolutionary” thinking, as you may be aware, including not a few well-meaning theists. To think that theology cannot be distorted by evolutionary thinking is not a position I accept, since there are examples available.
For myself, speaking generally here as an Abrahamic monotheist, the subfield of eVopsych appears to add little to nothing of value. Instead, it distracts from theology with biology and highly over-rationalized psychology. The subfield of eVopsych tries to explain religion as a “strictly natural” phenomeonon, despite what Barrett may suggest otherwise, with “hardwiring”, etc.
Trying to redefine “eVopsych” as a “potentially theistic approach to human history” seems self-defeating. Kinda like trying to create “Christian atheism” as a course of study, or even thinking that might be a good idea. As for me, I’ve never believed that trying to make a subfield whose intent on promoting atheism and disbelief in God was the initial motivation for creating the subfield, would turn out to be a good or helpful idea, but rather one destined for destruction.
Glad for your further response re: eVopsych after reading other critiques. It would most likely help if you found time in parallel to at least briefly address “sociobiology” as well, since that’s the precursor to “eVopsych”. Some people speak of it in the past tense now, for which I am not the only one who is thankful! 
Sociobiology (Stanford Encyclopedia of Philosophy)
Might try Lewontin’s work on this: https://journals.sagepub.com/doi/10.2190/7826-DPXC-KA90-3MPR
This one written by an impressive group, including Gould and Lewontin, provides a powerful message in rejecting sociobiology:
“Thus, we are presented with yet another defense of the status quo as an inevitable consequence of ‘human nature’.”
I happen to agree with the authors that,
“We must take “Sociobiology” seriously, then, not because we feel that it provides a scientific basis for its discussion of human behavior, but because it appears to signal a new wave of biological determinist theories.” Against "Sociobiology" | Elizabeth Allen | The New York Review of Books
The same holds true of the successor “eVopsych”.
Also see here for @paleomalacologist’s view of sociobiology: Evolutionary origin of religion - #64 by paleomalacologist
Welcome your insights, thoughts and preliminary conclusions after this additional material, which feeds into the topic.