There were three main Confederate flags. That was one of them. The confederacy seceded from the union in 1861 to 1865. Founded by conservative Democrats. The ONLY switch that was made was when they switched from conservative to liberal.
During the 1860s, Republicans, who dominated northern states, orchestrated an ambitious expansion of federal power, helping to fund the transcontinental railroad, the state university system and the settlement of the West by homesteaders, and instating a national currency and protective tariff. Democrats, who dominated the South, opposed those measures.
After the Civil War, Republicans passed laws that granted protections for Black Americans and advanced social justice. And again, Democrats largely opposed these apparent expansions of federal power.
Democratic President Franklin Roosevelt won reelection that year on the strength of the New Deal, a set of Depression-remedying reforms including regulation of financial institutions, the founding of welfare and pension programs, infrastructure development and more. Roosevelt won in a landslide against Republican Alf Landon, who opposed these exercises of federal power.
So, sometime between the 1860s and 1936, the (Democratic) party of small government became the party of big government, and the (Republican) party of big government became rhetorically committed to curbing federal power.
That's the only "switch" that happened.
