The Washington post article accurately summarizes the findings of a real scientific paper. The paper was published in a respected journal and presumably passed peer review.
The paper reviews a lot of other scientific literature that comes to the same general conclusion; In general, heterosexual women like muscular men. However there is some room for nuance. There are competing explanations for why, and various explanations of exactly which muscular men women like.
Evidence that this is a real scientific paper.
The paper discussed by the Washington Post was published in the Proceedings of the Royal Society B: Biological Sciences, a peer reviewed publication with a decently high impact factor. The authors of the paper have published on this general topic before, and those papers were cited by other scientists. In time, I expect this paper to garner citations of its own.
By contrast, fake scientific papers are published in predatory journals with no peer review. Those papers are not then cited by other scientists.
Examination of the claims in this question
In order to answer this question, read the paper in question and skimmed some of the scientific literature referenced by this paper.
“It's no secret that women like strong, muscular guys.”
There was no nuance to these results, he said. Zero of the 160 women surveyed showed a statistical preference for weaker men.
The researchers showed pictures of shirtless men with their faces obscured to a heterosexual women and asked the women to rate the men on both physical strength and attractiveness. The two quotes above were said by an author of this paper and accurately reflect their findings.
Are just 160 respondents really enough to generalize the idea and apply it to everyone in the world? Or should the article really say that the claim is definitely true for the heterosexual female population of the Griffith University?
The research paper presents data that are true for "student volunteers from Griffith University in Australia and Oklahoma State University students from the United States." (I just kind of assumed that the raters were heterosexual women, but I cant find that explicitly stated anywhere.)
The paper reviews the results of other studies about the same topic.
More directly on point with the hypotheses here, Franzoi & Herzog  surveyed women and asked them what features they were attracted to in men; the results showed that women particularly valued components of upper body strength, e.g. ‘muscular strength', ‘biceps'. Similarly, Jones and co-workers  showed that men whose bodies were rated as more ‘masculine' were preferred to men whose bodies were rated as ‘feminine', and a similar study using composite images confirmed that manipulating men's bodies to appear more masculine increased their attractiveness . Similar work shows that women generally prefer figures representing mesomorphic body types (i.e. muscular bodies) [42,43]. However, based on the aforementioned hypothesis that highly formidable men are relatively unwilling to invest resources in offspring, some researchers have suggested an inverted-U effect such that women prefer moderately strong men but not very strong or weak men [13,44].
The general consensus from this appears to be that muscular men are more attractive. There is a competing hypotheses described here; extremely muscular men are not extremely attractive. This paper did not really examine that hypothesis.
I did not personally go looking for articles that explicitly contradict these findings. I relied on the paper's literature review.
What about that one quote from a different researcher?
Instead, [sociologist Dr. Lisa Wade] says that culture, not evolutionary history, has the stronger influence over what is physically desirable. “We value tall, lean men with strong upper bodies in American society,” she said. “We’re too quick to assume that it requires an evolutionary explanation.” Shredded abs, she said, are more for show than any practical function.
Everything I have discussed up to this point has been describing what types of men women find attractive. This quote changes gears and asks why? This is a whole new can of worms. The research paper has quite a lengthy discussion about evolutionary preferences and why women like what they like, however they don't back up their explanations with strong evidence. Neither does Dr. Wade. Why is MUCH harder to answer than what.
At the end of the Washington post article,
Lukaszewski says his team plans to examine physical attractiveness around the globe. “We have a cross-cultural study that’s underway right now,” he said, one that included more than a dozen sites around the world.
Maybe in a few years, this study will add ammunition to one side of Wade and Lukaszewski's debate.