Short answer: the tuition is not "deductible," but some of the tuition might qualify for the Iowa "Tuition and Textbook Credit."
For years, I have told my clients that they couldn't take the Iowa Tuition & Textbook Credit if they sent their kids to a private religious school. Iowa law states that the credit can not be taken for tuition expenses related to the teaching of religious doctrines. A client challenged me on this, and I now see that I was wrong.
The Iowa tuition and textbook credit is a tax credit available on Iowa tax returns for qualifying expenses paid for K-12 education of a taxpayers' dependents. Almost any expense counts toward the credit. I went into more detail in this blog post from 2013. I generally tell people that only expenses paid to a public school, [...]