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.