Do you have scientific evidence for bias, or is this just normal culture-war rhetoric?
The solution - to the extent one exists - is pre registration. I see no evidence that this study was pre registered and thus the usual assumption that it has no meaningful protection from publication bias applies.
Here’s one of the very well known reports of potential impact in a well studied area (fda approval): https://www.nejm.org/doi/full/10.1056/nejmsa065779
Glancing at the paper the basics sound about right to me, but since the exact opposite conclusion would be far less tolerable and less likely to be authored and published, one can't help wonder what factors weren't considered for example.
If this happens to align with "culture-war rhetoric" from people I have no control over or relationship with so be it.
What you wrote might feel correct to you, but have you seen scientific research towards it? If you go by what you feel is right, how do you know you're not being manipulated? Seems like a perfect topic to divide people.
The further you move away from the hard sciences the harder it becomes to prove anything. Math, physics, and biology tends to be fairly easy as these things go; in medicine it already become significantly more murky, and with social sciences it's very hard indeed. I'm not saying there isn't a lot of valuable stuff in the social sciences, because there is, but "I will only accept what is scientificality proven" is a seriously limited view of things.
And yet it's an even bigger mistake to discount the idea of knowledge gain through the scientific process. Remember, we're not talking about two separate attempts to gain knowledge - we have one systematic but flawed attempt, whereas the opposite is simply not trying at all.
Just because you cannot exactly determine the mass of "bias in scientific publishing" doesn't mean you can't try to systematically study it, to find objective metrics by which you determine some order on some scale.
Just think about this from the other perspective. Is there any piece of knowledge you have that is fundamentally impossible to study scientifically? Is there an unwritten law of the universe preventing somebody from formulating a system by which emotionless judgement is denied? If not, why would you not want to see scientific evidence, to at least lessen the chances of you being fooled by the interests of others?