In reply to Viggo Tellefsen Wivestad.

1. The Pearson cutoff values are from Table 1 in Schober, Boer, and Schwarte. It is on p. 3 of the PDF (top of second column), as is the discussion of cutoffs. The corresponding cutoffs for the rank-based correlations are explained in my article. They are the expected values of the cutoff values under the transformation that maps the Pearson statistic to the rank-based statistics for bivariate normal data.
2. Yes, I agree with the statement that "values in-between are disputable." They will also vary by the scientific field: physics versus medicine versus social sciences, etc. I do not advocate using any one set of cutoff values. The article shows that IF someone wants to use cutoff values, there is a way to convert from cutoff values on the Pearson scale to analogous cutoff values for the rank-based statistics.