Region as a determinant of voting behavior

[King of Kensington]

To what extent does it determine voting behavior in US presidential elections, independent of race/ethnicity, religion/religiosity, urban/rural, educational attainment and so on?

[Starry Eyed Jagaloon]

Less than it used to. See the Driftless Area and Iron Range for more.

[Gracile]

Very little, as there is a high level of variance of voting patterns within a given region. The "type" of place in the region a given voter is from (i.e. urban and rural) as well as their demographics are far more important.

[clever but short]

Definitely much less than it used to. Demographics common in a region (ethnicity, religion, race, education levels) I think matter more than regions themselves, but can be hard to distinguish from region being the influence.

Edit: an example is white Evangelical Christians in the Southern US. This can be either seen as a correlation between white voters in the South being more Republican than those in the North, or it can be seen as correlation between white Evangelical Christians being more Republican than white voters who are not Evangelical Christians.

[King of Kensington]

South vs non-South or rural New England vs. rural areas outside New England are likely still factors.  But east/west and sunbelt/frostbelt no longer factors.