A very nice and balanced discussion of the issues involved in criticizing other researchers’ work on social media can be found in the article “How Should We Talk About Amy Cuddy, Death Threats, and the Replication Crisis?” by Jesse Singal at nymag.com.
A tweet that appears in the article succinctly summarizes one of its messages: “1. Bullying/Threats: BAD; 2. Scientific criticism: healthy”. Tone matters. A lot. However, the article goes on to say more:
“The more open and transparent science is, the less time researchers and observers will spend on hopelessly subjective questions of tone and intent. To be clear, there will never be a time when the questions raised by the replication crisis can be answered or evaluated in a purely objective manner, of course. Even when everyone has access to the data underpinning a given controversy, reasonable people, again, can and do disagree on which claims are warranted on the basis of which evidence.”
“But the faster we can get to an age in which data sharing and transparency in general are established norms in psychology, the easier it will be to avoid getting mired in unanswerable debates about really subjective subjects like tone.”