A number of states have “In God We Trust” plates. The thing that makes them far more common in Indiana is that there’s no specialty license plate fee for them, but they do have to be special-ordered, otherwise you get this.
Since no one has actually attempted to answer the OP’s question, I’ll make a brief stab. (Editing after preview: some of the following points have been made as I typed this out.)
Indiana’s primarily a rural state, and yes, heavily religious. There are a few blue/purple counties – Marion County, state-boundary cities that act as blue-color suburbs to larger cities in the neighboring state, such as Gary, IN for Chicago, IL. , and counties dominated by large colleges like IU. The red counties are rural and white-collar suburban, such as the eight counties that surround Marion County/Indianapolis. The red and blue populations statewide are tilted slightly in favor of red, but the blue areas are the most populous, urban, and industrialized counties.
In 2008, Obama was able to take the state due to a combination of Republican apathy, excitement for Obama, and an intense grassroots campaign. However, his election also triggered a very deep resentment among a lot of Republicans, and Tea Party views got a deep hold in local politics and reinvigorated Republican voters who had sat out 2008, which continues to be a popular influence locally… Richard Lugar, one of the most respected currently-serving senators, lost his primary to a Tea Party-backed candidate in 2012, even after Tea Party ideals seem to have been moderated somewhat in other states.
In addition, Mitch Daniels, the Republican governor reelected in 2008 despite a series of controversies (the IBM welfare boondoggle, toll road privatization, daylight savings time) has been seen in a far more favorable light thanks to a relatively healthy state economy during the recession (and the massive state accounting errors seem to have rolled off his back), luring and keeping manufacturing jobs, while espousing things like property tax reform, less union power/a push for “at will” employment, and budget austerity that ring true for Republicans. He’s seen as a mover and shaker in the larger Republican Party, and was recently tapped to become president of Purdue University, so there’s a bit of a halo effect that can make Hoosiers more predisposed to lean Republican if they may have been unsure before.
Finally, in this election, the continuing popularity of anti-Obama rhetoric has rallied formerly apathetic red voters; as many flubs as Romney has made, his campaign has been more sane than McCain/Palin, which will turn off fewer voters who tend red; and the Obama grassroots campaign is far less impressive than it was in 2008 (I’m thinking that they realized 2008 was a fluke, and they’re not sinking as much money in to a state that barely went blue when they held more of the cards).