Actually, there are two, big fat reasons that it's not a conflict. One is just basic logic, and the other is original intent.
First, let's look at the basic logic:
1. The money that Prison Fellowship will repay is money received for providing a service. The state arranged for this group to provide a number of services to the state, many of which would occur in a purely state-run prison, and reimbursed them for it. Treating this as if the state of Iowa made a donation to Jimmy Swaggart is not accurate.
2. Prisoners enter this program voluntarily. To say this program has a conflict is like saying that an afterschool Bible club has a conflict. In both cases, state money is being used to support willing participants in a religious practice. Should the kids in the Bible Club have to pay the school district rent, while the Spanish Club, Chess Club and Freethinkers Club get off scot free, or can they all use the facility?
In fact, check this out: If a voluntary program like this is off limits, then any religious service or ministry visit to a prison would also be off limits. No prison chaplain, no prison chapel, no Angel Tree program, etc. If the prison holds a service and a prisoner is saved, tax dollars supported it by paying for facilities, security and (possibly) the salary of the preacher who conducted the service. Ready to pull the chapels out of prisons? How about AA and Narcotis Anonymous programs, which require the member to accept the guidance of a higher power?
3. Iowa has decided that they want their prisons to rehabilitate. The InnerChange program is astoundingly successful at rehabilitating compared to other programs. The court is saying that the state must choose to run their prison in a way that guarantees fewer prisoners will become productive, law abiding members of society, and presumably this ruling would apply even if they had a program for members of every single religion. In fact, it would not be a stretch to see a court saying that a program designed by a psychologist that has a 50% recidivism rate is acceptable, but a program jointly designed by a Buddhist, a Southern Baptist and a Hindu with an 8% recidivism rate is not, because they expect the attendees to acknowledge a spiritual dimension, or because it requires addicted prisoners to go through a 12 step program. The court is telling the state "the Constitution says you must screw up." I don't think that's in there.
Now let's take a look at original intent. I'll even restrict my discussion to one Founder.
When Thomas "Wall of separation between church and state" Jefferson was President, he attended church in the U.S. Capitol. Note that one of the times he attended was just two days after he penned the "wall of separation" letter to the Danbury Baptists. He had authorized the use of the Capitol for this purpose in a joint decision with the Speaker of the House in 1800. He had the Marine Band play at services there. He authorized church services held in the Treasury building and War Department. He entered into a treaty with the Kaskaskia tribe that required the United States to fund a Catholic priest to minister to them. The Senate ratified it without any controversy that I'm aware of.
Oh, and BTW, church services continued at the Capitol until wll after the Civil War, even though there were 22 churches in Washington by 1837.
If Thomas Jefferson, arguably the least Christian of the Founders and the man who gave us the phrase "separation of church and state" thought it was OK to preach sermons in federal buildings and pay a priest's salary from the treasury, why should we believe that it's not OK to have some prisoners voluntarily enter a religious-themed anti-recidivism program?