How do you get the shower diverter stem out of the tap casting on an Indiana Brass shower diverter if the brass nut comes off but not the stem and the stem is not threaded and rotates 360 degrees?

Depending on the brand, there are 2 brass nuts. 1 is the one that holds the packing down around the stem so it won't leak (this is the easier of the 2 to get to & probably the 1 you've taken off) The 2nd one is larger (close to an inch) and it's the one that hold the valve stem in the body of the valve.