I'm not sure the military chaplaincy argument holds up when compared to prisons. Prisons and prisoners are far more accessible than are soldiers, particularly if they are on duty in a hostile area.
On the other hand, any citizen can at any time get permission to visit any prisoner with that prisoner's consent (if the prisoner is in good behavior).
In short, the chaplains in the military were a rough solution to very extreme circumstances. However, there do not seem to be such extreme circumstances here, and as others have noted, there are a wide variety of churches who offer such services without using taxpayer money.
I believe the money was for the programs that resulted in the positive change results.
I'm sure, though, that the programs are themselves religious in nature. However, they are programs that are otherwise available to every other American who desires to participate in life change seminars, counseling, etc.
That makes it part of FULL religious practice.
I suspect that no one else is offering it for free if it costs so much.
Having your pastor visit the prison is not the same as running a successful, resourced change program.
I could make a case...but I do agree with you that one has to stretch to apply the military situation to the prison population. A smart lawyer could do it, however.