Our rector doesn't like the cabinet door inserts - she isn't a fan of the caning. To me, this wood looks like hickory, finished in natural. It could be pecan. The gentleman who made it has since passed on and the parish that had the cabinet has closed. If it is hickory, I'd go ahead and make some panels and take the caned panels out. The cabinet was made in North GA, near Dalton.
Look at the end grain with a 10x loupe. Hickory (and pecan, which is a hickory) are strongly ring porous, while sweet gum is diffuse porous. There are good photomicrographs of both on The Wood Database, wich you can find by searching for "hickory end grain" and "pecan end grain."
My first impulse looking at the picture was hickory. And pecan and hickory are lumped together in the market. The more I look at it the less sure I am. I suggest following the instructions to look at the end grain.
Section Seven in this article has instructions concerning end grain examination. The first thing is to establish if it's ring porous, diffuse, or semi-diffuse.
The section Still Stumped shows where to send samples for analysis. Sometimes a small sample can be removed from a hidden place. They don't need much.
As for ID by photo of the wood, this site might be interesting, both to explore guesses and to see the incredible variation within a single candidate species.
I bought a Sweetgum slab and made a head board out of it. I have half of it left. I could take a picture of both the head board and the remnant slab and send them to you. If it looks like something you could use I would be glad to share.