Here are maps showing how a federation of red states would differ from the US. But after all the drama of secession, the federation will certainly not grant much power to a central government, so culture will be up to state governments.
The black line is the predicted border of the red-state federation (which is in the middle, plus Alaska). The colors reflect the data of the underlying data that I’m drawing a border on.
Below are the borders we drew on all the other maps.

Some states might organize into groups to allow freedom to relocate (residency) within groups of states, instead of only within the state itself.

A federation of red states would have more church members per capita than the US does.

A federation of red states would have more whites per capita, especially when recent immigrants are denied red-state citizenship, even if they have US citizenship Also, many Dems & blacks tell pollsters they’d “definitely” move out of a seceding state, & vice versa.

A federation of red states would be more anti-immigration than the US is. They’re red states, so they’d agree with any GOP plank more.

As of 1910, there were fewer foreigners per capita in the future red-state federation. This means more antebellum founding stock.

A federation of red states would have more fertility than the US

A federation of red states would have more white evangelical protestants per capita than the US

Who would win the next civil war? Civilian gun owners outnumber federal infantry by a hundred to 1 But since 1945, 87% of secessions around the world have been peaceful (out of 134 national secessions)

Most federal troops are loyal to their homes in the red states anyway BTW, a poll found that only 7% of Americans think fedgov should attack a seceding state

A federation of red states would have fewer non-religious people per capita than the US

A federation of red states would be more oil-rich than the US is.

A federation of red states would have more Bible searches than… certain searches

Red states are different. More dog owners than cat owners.

A federation of red states would be less Hispanic (and less Asian) than the US, even before future migration & deportations.
Not obvious on this map, but most Hispanics live in big cities, which are in blue states. Plus, Texas might opt to be independent from any union of states.

This map is old, but in 2016 the Trump states had much more manufacturing than the Hillary states

A federation of red states would be more religious than the US

A federation of red states would have more red-heads per capita than the US

A federation of red states would give a lot more to charity per capita than the US

A federation of red states would have more disposable income (purchasing power parity) than the US, because of lower state taxes and lower cost of living This meme was saved 2017, but we tabulated it out more recently.

What other differences can you name? What did I miss?
Help the Texas Nationalist Movement and Free Louisiana lead the red states out of the Union. Their voters poll in favor of secession, so we just need to get their legislatures to hold a referendum. Once they go, others have to join to avoid blue-state tyrants.