Pet Peeve Alert!
/rant incoming: No there is not way under your posted guidelines that would result in this map. Why? Because if the US was divided by a "Civil War" then all those nice straight-ish 'borders' between the States are gone! Sorry but I really dislike such "maps" because they don't reflect the scenario that most people (yourself included) want. While it makes drawing the map somewhat easier, it discounts such things as the terrain and likely "belief" boundaries where like minded people will tend to stick together rather than be divided by some arbitrary lines on a map. Then there are population numbers which are rather low towards the mid-west, and higher on the coasts
/rant over... Hopefully
As to how to get to the map that's a tougher one because getting America to violently splinter after 1900 is questionable. Prior to the
Spanish-American war most people didn't identify as "Americans" but by what State they from. After the war it rapidly became common for people to identify as "American" first and State second.
As for the nature of the split given (Socialist and Capitalist) huge amount depends on what the side were for the "Civil War 2.0", when that took place and the general outcome. If you're wanting it to be Socialist versus Capitalist your going to have to explain how the split came about. It's not impossible to get a major "socialist" movement to gain popularity if some crisis happens which causes a lot of people to question the idea of American "freedom". One of my go-to examples is if the Great Depression is deeper and badly handled by the Federal Government a kind of "Christian Socialism" or "Christian Communism) is possible and could be popular enough to cause a split.
But in general it's very hard to give a good scenario when we don't know the full background.
Randy