When should some research be censored/blocked due to social implication concerns? My question is motivated by this article, that talks about the publication process and failure related to this paper. 

As a Summary, it is research on a mathematical model to explain the greater male variability hypothesis, that is the hypothesis that males display greater variability in traits than females do.

The paper was censored because there is a “very real possibility that the right-wing media may pick this up and hype it internationally.” 

Hence, when should some research be censored/blocked due to the social implications of it? 



I've found two related, but no the same, questions in here:

Akin to public health: 

When should academic papers be censored due to public health/safety concerns?

Akin to opinion outside research: 

Academic freedom and unpopular or offensive views
In general, research should not be censored.

It is, of course, generally accepted that research methods should be subject to ethical limitations.  Likewise, at some point there is a distinction between scientific investigation and the engineering of dangerous things like nuclear weapons and zero-day code exploits where society generally agrees that it's better to not put these capabilities into the hands of every random individual.

That's not really what you're asking about, though. What you're asking about are studies that look into the differences between groups of people that society already treats differently.  Whenever somebody goes to publish a paper on the differences between men vs. women or blacks vs. whites or homosexuals vs. heterosexuals or any similar category, this is a paper that should rightly be treated with great suspicion.

The reason, however, is not that there is some politically correct conspiracy or societal engineering agreement in academia.

Rather, it is the exact opposite: due confirmation bias and similar effects, there is an unfortunately long history of scientific investigations that purported to prove that horrible injustices were actually appropriate.  Over and over, people search for justifications for societal structure or pre-existing beliefs, often mixing up cause and effect (e.g., having characteristic X is bad for your health vs. being treated badly is bad for your health, and your society treats people badly if they have characteristic X). Moreover, such studies have often been embraced by larger society---even despite countervailing evidence---and this pattern has caused (and continues to cause) massive amounts of harm to massive numbers of people.

Thus, any honest investigators with an understanding of the history of their field should look at studies like the one you reference in your question with great suspicion.  No censorship need be involved---but it's entirely reasonable for peer reviewers and other gatekeepers to be exceedingly careful and stringent about what they choose to endorse as being scientifically valid.