The post WW2 boom was without historical precedent in our history, so which do you think represents the normal case and which the outlier?
Your argument was that inequality is the result of economic growth. It seems like there needs to be a pretty hearty explanation for why the largest period of economic growth in our history had the exact opposite effect, no?
Also, income inequality has been on the rise in basically every wealthy country, how would you explain that? Is it because France, Germany, Sweden, Italy, and other countries have Republicans in charge also?
Who brought up Republicans?
Or perhaps the key to growth is economic freedom instead of inequality. Compare the two tables and tell me which you think is the stronger effect and why. It would also be helpful if you can find a chart which supports your point that has actual data quality metrics such as R squared. Even just eyeballing the two charts it seems the R Squared for economic freedom is a lot stronger correlation than inequality.
First, I would say that your chart still clearly shows a negative effect on growth from increasing inequality, although I'm not sure why they only included developing countries.
As for the Economic Freedom Index, that index is basically junk economics, designed for a predetermined outcome. (it's a product of the Heritage Foundation) For some examples of various problems with it:
1. It rates tax burden on top rates, not the rates people actually pay. It should be obvious why that's a bad idea.
2. It counts rate of change in government expenditures, not their absolute amount. So for example, if I spent $1 last year on welfare and you spent $1,000 and then I went from $1 to $5 and you stayed the same, I would be viewed as having the more burdensome welfare state. That's illogical.
3. Worst of all, it says that the larger your informal economy is, the less free you are. As poor and less developed countries have larger informal economies basically by definition, you get bonus points for simply being a more prosperous country.
4. Finally, many of its results are manifestly insane. It rates many of the fastest growing countries in the world as the least free.
It is a very, very silly index.
EDIT: Additionally, your two charts cannot be compared to one another. The first is looking at GDP growth rate to Gini coefficient while the second is comparing the EFI to absolute GDP. They are two very different things.