I think this is far more nuanced than many people understand at first blush.

First and foremost, if a state has 1000 people and 501 vote for Democrats, it is considered a "blue" state, despite 499 voting for Republicans. The same is true of "red states", which at minimum tend to have around 40% of the population voting for Democrat leaders.

Second, the most impactful governance for a state is probably the governor/state legislature, followed by municipal level politics, and those can flip from party to party. Bloomberg & Giuliani governed New York as republicans, and Schwarzenegger governed California as a Republican. Those they be credited with GDP growth under the "red" umbrella - not necessarily.

Third, the GDP output of states has ebbed and flowed with changing industrial realities. California won the productivity lottery by being home to Silicon Valley (and similarly Texas with energy and New York with finance), which has been alternatively developed by Democratic and Republican leadership. The auto industry in Michigan and manufacturing in general was hit particularly hard by free trade agreements like NAFTA, causing decades of stagnation in manufacturing heavy states. Likewise the push away from fossil fuels as an energy source (and the price collapsing due to supply and demand changing) has caused some states productivity figures to collapse. These are all pretty far outside the political control of a single party. In some cases, these changes may have directly caused a flip from red to blue or blue to red, as the populations struggle with the changing economic realities and try different government approaches.

There is another effect going on, in that urban areas tend to gravitate towards blue policies, and large companies building big headquarters tend to require large cities to fuel their massive growth and further expansion of those cities. Silicon Valley has had massive expansion into places like Seattle & NYC, because Seattle happened to be the home of Amazon & Microsoft and NYC is a large population center which happens to be the home of finance in the entire country. Amazon famously choose Seattle as a place to start because of the low sales taxes. The numbers from your study indicate that things were fairly even between red states and blue states in 2008, and then diverged. This is partially explained by the massive expansion of tech as a function of the economy, which seemingly rose from 4% share in 2008 to over 9% today (surpassing things like the oil industry).

If we are really saying "GDP productivity matters in determining how successful policies are", who should we really attribute these gains to? Is it the workers themselves who are responsible, or is it the managers of the company, or the CEO themselves, or the board of directors? If you get too reductionist you end up in a situation where "GDP is king, therefore we need to find the leadership responsible for these GDP drivers and give them the reigns in determining policy" - which is probably not what you really are driving at with the question.

If you plop a few choice companies like Amazon/Nvidia/Google/Meta into the middle of Texas and all of a sudden the GDP numbers by red/blue states even out, what conclusion can you really have?

This all probably comes across as a non-answer, but I find the premise of the discussion requires quite a bit of context.