When I encounter popular reporting on scientific claims, I have a checklist that I go through to check its credibility. I do not try to evaluate their methods myself, because I cannot rigourously critique science outside of my own field.
- I have read the paper, and found that the paper matches the Guardian
- The paper has a lengthy literature review, which indicates that the authors have at least a basic knowledge of the field and respect for scientific norms.
- The paper making the claim is peer reviewed in what appears to
be a reputable journal.
- The authors, Peterson and Palmer, are professors of
political science with previous scientific publications on related topics.
They do not appear to be cranks.
All of the above is encouraging. I will take their research seriously, but science can be messy or wrong and studies can find false conclusions. I usually don't fully believe a result unless it is reproduced and there is a scientific consensus behind it. Unfortunately replication studies are pretty rare, and it is unlikely that someone else will replicate this. For now, we have to be content with seeing how other scientific authors cite this paper, which functions as a secondary peer review.
In the year and a half since this article was published, 5 other publications have cited it, however none of these appears to be a scientific journal article. I don't see any evidence that any of them are peer reviewed at all.
- This one is a scientific criticism of another paper. It cites the claiming paper uncritically in passing.
- This scientific-seeming mini-article doesn't appear to be formally published, and it cites the claiming paper with hedging words; it doesn't seem like an endorsement of the conclusions.
- I cannot find the citations in the other of the 3 citing publications.
None of these citations gives me confidence one way or the other. It is not super surprising that there are no peer reviewed publications that have cited this paper yet. Research and peer review is a pretty slow process and it may take a few more years. If you are reading this answer in the future, the above google scholar link should update automatically.
Conclusion: This paper follows the standard scientific process, which is encouraging. However, to know if the science is solid we have to wait for either replications, which will probably never happen, or other researchers to build upon this work. Until then we can't really know if the conclusion is real.