A confusing tweet on (not) transforming data keeps reappearing on the internet

I keep seeing this misleading comment on the internet over and over again:

Non-normality is relatively unimportant; at worst you just may lose a bit of power. I strongly recommend @StatModeling & Hill (2007, pp. 45-47)'s summary of key regression model assumptions. Normality of errors literally gets LOWEST priority. My experience supports this. 3/3 pic.twitter.com/R0BfQCoxdK

— Roger Levy (@roger_p_levy) December 8, 2018

Gelman is cited above, but Gelman himself has spoken out on this point and directly contradicts the above tweet: https://statmodeling.stat.columbia.edu/2019/08/21/you-should-usually-log-transform-your-positive-data/
Even the quoted part from the Gelman and Hill 2007 book is highly misleading because it is most definitely not about null hypothesis significance testing.
Non-normality is relatively unimportant in statistical data analysis the same way that a cricket ball is relatively unimportant in a cricket match. The players, the pitch, the bat, are much more important, but everyone would look pretty silly on the cricket field without that ball.
I guess if we really, really need a slogan to be able to do data analysis, it should be what one should call the MAM principle: model assumptions matter.

Book: Sentence comprehension as a cognitive process: A computational approach (Vasishth and Engelmann)

 

My book with Felix Engelmann has just been published. It puts together in one place 20 years of research on retrieval models, carried out by my students, colleagues, and myself.