Do you have any sources for that claim? I would be genuineley interested in the methodology of this research. Its just anecdotal, but here in Germany it is the other way around. The Catholic south is prosperous, whereas the protestant north (east) is poor. I can think of examples where the opposite is true (Belgium) but I highly doubt that there is a casual connection. In Belgium for example the catholic (and more important industrialized) wallonia was very prosperous during the 19th century, in opposition to the more agrarian flanders. Nowdays its flanders that is more prosperous, and the old industrial regions in the south suffer from the effects of deindustrialisation.

That is not really true. It ignores that in many of the states where this is true, there were very many other cultural differences, and also differences in the laws that they were working under.

I don't think this line of research hold up very well, specially not cross country over long timeframes.

I think you're confusing economic differences between the US South (very not-catholic) vs Northeast (very catholic) as being caused by the religion when there are a bunch of much more important differences, economically speaking, you could look at.

Take a look at total GDP per capita, the northeast is way ahead. Different metric, different results, still not caused by religion.

Correlation vs causation. Does protestantism improve productivity, or did the cultures where productivity is valued highly more easily convert to protestantism?

How do you explain Bayern in Germany then?

Have you ever heard of Bavaria? Also called Germany's Texas.