sources copied from "top comment" and re-reported here:

sources
– incarceration
https://www.sentencingproject.org/the-facts/#map
diversity*
– diversity* = Catholic% + Jewish% + Muslim% + Asian%
– Catholic, Jewish, Muslim populations: https://www.pewforum.org/religious-landscape-study/compare/religious-tradition/by/state/
– Asian population: https://en.wikipedia.org/wiki/Demographics_of_Asian_Americans
tool: Mathematica

***************

– the ellipses are centered on the Rep/Dem means;
the standard deviations are represented by the ellipses' axes
– the 50 plot points represent the (diversity^*, incarceration) coordinates for each state; and are colored according to their 2020 Electoral College vote
– "r" is the Pearson correlation value

... see the definition in the "top comment" ("sources")

... they aren't: it is the Dem state avg which is twice the Rep state avg

... actual %s for VT, NH, TX, FL: 26, 31, 29, 27

It i interesting that those northern Dem states (VT, NH) have 'same' % diversity* as the southern Rep states (TX, FL), eh?

https://bjs.ojp.gov/content/pub/pdf/p20st.pdf

see table 3 on page 10

best-fit lines, correlations: incarceration vs diversity*

1. Purpose
   In order to 'understand' the non-random, top/bottom, Rep/Dem differentiation of metric values, eight "response" metrics are correlated with three "predictor" metrics. This post presents the 'response' variable incarceration vs the diversity* 'predictor' metric.
   ... the eight "response" metrics: GDP, state taxes; suicide rate, opioids; life expectancy, infant mortality; incarceration, state+local ed spending;
   ... the three "predictor" metrics: 'rural-urban', evangelical, diversity*
2. the "big picture"
   i) There is a non-random, top/bottom, Dem/Rep pattern. Patterns have reasons/causes and are mathematical.
   ii) Rep states are always on the negative side (less GDP, more suicides, lower life expectancy, etc).
   iii) How did 150 million voters, acting individually, separate the fifty states into two such disparate groups?
   iv) is there a "predictive" metric or combination of metrics which can be used to explain the characteristic Rep/Dem differences seen in the data?
3. general comments
   i) Dem states are twice as "diverse" as Rep states
   ii) for both Rep states and Dem states: as diversity* increases, the incarceration rate decreases; though the Dem states 'best-fit' line is more convincing (has a larger r-value)
   iii) Hawaii has the largest diversity* rating – due to its large Asian population

sources
– incarceration
https://www.sentencingproject.org/the-facts/#map
diversity*
– diversity* = Catholic% + Jewish% + Muslim% + Asian%
– Catholic, Jewish, Muslim populations: https://www.pewforum.org/religious-landscape-study/compare/religious-tradition/by/state/
– Asian population: https://en.wikipedia.org/wiki/Demographics_of_Asian_Americans
tool: Mathematica

***************
– the ellipses are centered on the Rep/Dem means;
the standard deviations are represented by the ellipses' axes
– the 50 plot points represent the (diversity*, incarceration) coordinates for each state;
and are colored according to their 2020 Electoral College vote
– "r" is the Pearson correlation value

I found data from the StLouis Fed Reserve and from the sentencing project source ... I will work something up

It would be a plot of black/white income ratio VS black/white incarceration ratio using the Rep/Dem state differentiation.

... thanks for the suggestion – it should be interesting

1
... the posts do have a uniform style; but the content of each post is unique

2
... the purpose of the post is explained in a previous comment: to repeat: there is a non-random top/bottom Rep/Dem differentiation of the data; in which, the Rep states are always on the negative side. This generality is worth noting and, even more worthy, is an investigation using other metrics to (maybe) unearth an explanation.

Montaigne, "Of Pedantry": has a quoted comment– 'I hate above all pedantic learning'; to which he adds – We labor only to fill our memory, and leave the understanding and conscience empty.

3
... this Rep/Dem differentiation has been noted elsewhere:
– https://www.thirdway.org/report/the-red-state-murder-problem
(see post 08Jul2021)
– https://www.theguardian.com/us-news/2022/oct/27/life-expectancy-us-conservative-liberal-states
(see post 29Jul2021)

1. Purpose
   In order to 'understand' the non-random, top/bottom, Rep/Dem differentiation of metric values, eight "response" metrics are correlated with three "predictor" metrics. This post presents the 'response' variable incarceration vs the evangelical 'predictor' metric.
   ... the eight "response" metrics: GDP, state taxes; suicide rate, opioids; life expectancy, infant mortality; incarceration, state+local ed spending;
   ... the three "predictor" metrics: 'rural-urban', evangelical, diversity*
2. the "big picture"
   i) There is a non-random, top/bottom, Dem/Rep pattern. Patterns have reasons/causes and are mathematical.
   ii) Rep states are always on the negative side (less GDP, more suicides, lower life expectancy, etc).
   iii) How did 150 million voters, acting individually, separate the fifty states into two such disparate groups?
   iv) is there a "predictive" metric or combination of metrics which can be used to explain the characteristic Rep/Dem differences seen in the data?
3. general comments
   i) for Rep and Dem states: incarceration rate increases as evangelical increases; slopes are large and r-values are large
   ii) the Dem r-value is larger than Rep r-value
   iii) the large Rep and Dem slopes indicate that evangelical impact on incarceration is significant
   iv) evangelical impact on all response metrics appears to be the most influential of the three predictor metrics:
   GDP vs evangelical, posted 06Jan
   state taxes vs evangelical, posted 03Feb
   suicide rate vs evangelical, posted 03Mar
   opioid dispensing rate vs evangelical, posted 12may
   life expectancy vs evangelical, posted 06Aug
   infant mortality vs evangelical, posted 01Sep

sources
– incarceration
https://www.sentencingproject.org/the-facts/#map
– evangelical population
https://www.pewforum.org/religious-landscape-study/religious-tradition/evangelical-protestant/
tool: Mathematica

***************

– the ellipses are centered on the Rep/Dem means;
the standard deviations are represented by the ellipses' axes
– the 50 plot points represent the (evangelical, infant mortality) coordinates for each state;
and are colored according to their 2020 Electoral College vote
– "r" is the Pearson correlation value

1
the top left plot is the incarceration rate of the fifty US states ... the states are not identified because it is not important ... what is important is the states' Electoral College vote in the 2020 election

2
the top right plot is the 'rural-urban' value of each of the fifty states (see the "top comment" for the definition of 'rural-urban')

3
the bottom plot is a plot of the ('rural-urban, incarceration) coordinates of the fifty states

4
the important point to see is that the best-fit line slopes of the Rep states and the Dem states are oppositely directed and that the Dem states correlation value is "less noisy" than the Rep states correlation value

best-fit lines, correlations: incarcerationvs 'rural-urban'

1. Purpose
   In order to 'understand' the non-random, top/bottom, Rep/Dem differentiation of metric values, eight "response" metrics are correlated with three "predictor" metrics. This post presents the 'response' variable incarceration vs the 'rural-urban' predictor metric.
   ... the eight "response" metrics: GDP, state taxes; suicide rate, opioids; life expectancy, infant mortality; incarceration, state+local ed spending
   ... the three "predictor" metrics: 'rural-urban', evangelical, diversity*

2. the "big picture"
   i) There is a non-random, top/bottom, Dem/Rep pattern. Patterns have reasons/causes and are mathematical.
   ii) Rep states are always on the negative side (less GDP, more suicides, lower life expectancy, etc).
   iii) How did 150 million voters, acting individually, separate the fifty states into two such disparate groups?iv) is there a "predictive" metric or combination of metrics which can be used to explain the characteristic Rep/Dem differences seen in the data?

3. general comments
   i) the Rep states r-value is about half of the Dem states r-value; the r-value of Rep states indicates Rep data is "noisy"
   ii) however, the best-fit lines show Rep/Dem difference: as Rep states become more "urban", there is increasing incarceration; as Dem states become more "urban", there is decreasing incarceration

sources
– incarceration: https://www.sentencingproject.org/the-facts/#map
– rural-urban: population density https://www.states101.com/populations
– agriculture income: https://data.ers.usda.gov/reports.aspx?ID=17839#P9dd070795569412d9525def18d45bde2_4_185iT0R0x0
– state GDP: https://apps.bea.gov/regional/downloadzip.cfm
method for "rural-urban" metric
– population density and agriculture income data values were converted to "standard scores", aka "z-scores":
z-score = (data value – mean)/SD
– the z-scores were added and divided by 2; result = the rural/urban metric z-score
– note1: 'urban' means "increasing population density"
'rural' means "increasing agriculture income as % of state GDP"
for the 'rural' metric to denote a "rural to urban" value,
the z-scores for agriculture income were 'reversed' by multiplying by "–1"
before adding to the population density z-scores
– note2: "NCE" is "normal curve equivalent" (see Wikipedia, "Normal curve equivalent")
tool: Mathematica

***************
– the ellipses are centered on the Rep/Dem means;
the standard deviations are represented by the ellipses' axes
– the 50 plot points represent the (rural-urban, incarceration) coordinates for each state;
and are colored according to their 2020 Electoral College vote
– "r" is the Pearson correlation value

I am sure that it can, but ... defining the 'predictor' metrics becomes more difficult and, therefore, more prone to "what about ...." arguments which devolve to denialism.

... some person with more courage than I would need to do it and it would be pleasurable to read, I am sure.

... yeah, you are right

best-fit lines, correlations: infant mortality vs 'predictor' variables

1. Purpose
   In order to 'understand' the non-random, top/bottom, Rep/Dem differentiation of metric values, eight "response" metrics are correlated with three "predictor" metrics. This post presents the 'response' variable opioid dispensing rate vs the three 'predictor' variables.
   ... the eight "response" metrics: GDP, state taxes; suicide rate, opioids; life expectancy, infant mortality; incarceration, state+local ed spending;
   ... the three "predictor" metrics: 'rural-urban', evangelical, diversity*
2. the "big picture"
   i) There is a non-random, top/bottom, Dem/Rep pattern. Patterns have reasons/causes and are mathematical.
   ii) Rep states are always on the negative side (less GDP, more suicides, lower life expectancy, etc).
   iii) How did 150 million voters, acting individually, separate the fifty states into two such disparate groups?
   iv) is there a "predictive" metric or combination of metrics which can be used to explain the characteristic Rep/Dem differences seen in the data?
3. general comments
   i) The plots present means, standard deviations, the 'best-fit' lines, and r-values for Rep and Dem states.
   ii) The evangelical metric most closely correlates with infant mortality (Dem r = 0.49, Rep r = 0.42).
   iii) Both Rep and Dem states' r-values, using the diversity* predictor metric, are essentially equal.
   iv) It is curious that as Rep best-fit line becomes more 'urban', infant mortality increases; yet, the standard expectation is that as 'urbanity' increases, infant mortality would decrease as is seen in the Dem best-fit line. However, the absolute values of the r-values is small, indicating 'noisy' data.
   v) The evangelical plot for both Rep and Dem states: increasing evangelical % increases infant mortality.
   vi) The diversity* plot for both Rep and Dem states: increasing diversity* decreases infant mortality.
4. Similar plots using the three 'predictor' metrics have been posted:
   for GDP (20Jan), state taxes (17Feb), suicide rate (17Mar), opioid dispensing rate (26May), and life expectancy (18Aug).