Tackling mainly your broader question about why the Klan was strong in a Northern state that had been part of the Union, than specifically Indiana (for which there is certainly much more to say), there are two critical things to keep in mind.

First is that while inspired by the original Klan, the Klan of the early 20th century was a separate organization, and it made great efforts to expand itself nationally. While it absolutely engaged in disturbing displays of racism and nativism, it ought not be understood as a paramilitary organization such as its predecessor, but rather a fraternal organization that included millions of Americans nationwide.

Second then is the fact that it had national appeal. White, Protestant America was really, really racist back then, and the Klan's doctrine of '100% Americanism" was one which easily transcended the South. And if it also worth adding beyond that that while plenty of white Americans did not like the Klan, while some did so out of some level of actual anti-racist sentiment, many were put off with the perception of the Klan being too gauche in how they went about their business, but nevertheless would have agreed with many of their views about race, religion, and nationality.

For deeper readings on this, and what the Klan was about - both in Indiana, as well as other non-Southern communities of the period - I have a few previous answers I would point to. This one is about the Klan in the Midwest so might be of particular interest, while this one should also be of great interest as it looks at the Klan as a political entity of the period some of their platform. This talks a little bit about them in New England, and this one places them in the context of other fraternal organizations of the period such as the Masons.

This addresses a fraction of your question, mainly "Why Indiana?" rather than an in-depth look at how the Klan conquers communities.

TL;DR Poor white Protestants pushing west first competed with Yankees (New Englanders) for land, and later with the rising tide of black emigres following the war. The Klan played on their religious convictions and phobias about immigration, eventually winning public office and instituting effectively a "Klan state."

In the first half of the 19th c., poor whites mostly from VA and KY were pushed west to Ohio and Indiana. Scots-Irish, they were largely Baptist, anti-Catholic, and intensely rural. Their motives were largely economic. Contest for cheap land became a bitter one as "Yankee" New Englanders also moved to take advantage of low land prices. These were other Protestants, such as northern Presbyterians, many of whom were abolitionists. They could afford more acreage and invest more in their farms and ranches, pushing their poorer neighbors further into southwest Indiana and painting the northern and eastern parts of the state more Union-friendly than they had initially been. This proceeded through the Civil War.

This is to say that the stage was already set with poor, anti-Catholic, anti-immigrant white families originally from border states who were hostile to wealthier "Yankees," ticking all the boxes to attract Klan advertisement.

Indiana, itself, was not "solidly loyal" to the Union. There were several proposals to protect and even reinstate slavery which fell through, but nevertheless had moderate support, especially in rural communities anxious about economic competition from freedmen. Following the war, black farmers sought the same economic and political freedoms the poor whites of the early 19th c. had, many immigrating to Indiana. Segregation efforts were immediate, but nowhere near as severe as Jim Crow.

As for the Klan:

The KKK likes to cloak itself as a Christian organization, which attracted Indiana Baptist communities near the turn of the century with promises of Christian governance and an economic revival - playing heavily on fears of Catholics, immigrants, and POC. For all they offend, the KKK are, and have historically been, masters at selling themselves. DC Stephenson is your Indiana man for the rise of the Klan into the 1920s.

Sources:
Battle Cry of Freedom, James McPherson
What God Hath Wrought: The Transformation of America, 1815–1848, Daniel W. Howe
Segregation in Indiana during the Klan Era of the 1920's, Emma Lou Thornbrough