The most comparable state to Indiana is probably Ohio. But Ohio is less rural, has a little more black population, and its white population is a little more descended from Eastern and Southern European ethnics than is Indiana's (another way of stating this last point is that Ohio whites are more Catholic than Indiana whites). Indiana's economy is doing better and has for awhile, so it has more suburb growth and younger families with children. Both are correlated with voting more Republican.
There is a great deal of truth to this, but the histories of each state are quite different. Through much of the 20th Century, Ohio was one of the nation's megastates; it was heavily industrialized and, beginning in the New Deal era, highly unionized. At one point, Cleveland was the fifth largest city in the nation. Even today, despite the decline of Cleveland, Ohio has three Metropolitan Statistical Areas (Cinicnnati, Cleveland and Columbus) that are larger than Indianapolis. And, as you note, Ohio was far more of a destination for immigrants early in the century, many of whom were from Eastern Europe, drawn there by an abundance of factory jobs in urban areas. Toledo, Cleveland, Akron and Youngstown drew many of them.
By comparison, Indiana never reached the level of industrialization or urbanization of Ohio. More importantly, Indiana politics was never influenced by unionization to the degree Ohio was and, along the I-80 corridor, still is.
These trends all created something of a divergence in the politics of each state in the first few decades of the 1900s; Indiana remained predominantly Republican while Ohio achieved something close to parity as urban Democrats grew in number.