How long have the cedar panels been up? Decades or a few years? Is there any area that still has a nice original finish, say, with shiny spar varnish (used for wood yachts) or matte finish with some sort of sealer?

You may be able to sand off the soap scum with a "delicate care" Scotchbrite sponge (or a half dozen of them), sand again to get a very smooth finish, then apply three coats of finish or sealer. Switch to liquid soap to avoid forming soap scum caused by the reaction of bar soap components with minerals in your water. A few seconds of quick swiping with a dry towel will help prevent buildup. Here's an article that may give you some ideas: http://www.small-cabin.com/forum/2_1422_0.html

Here is spar varnish on a porch floor:

Porch Rebuild · More Info

It is time to be thinking about a redo. Never use oil soaps on any wood. You will need to sand down to 100% bare wood to refinish it now.

Thank you both for your great ideas. I guess I will have to find someone to do the sanding and varnish. I am not sure if there was any finish on the wood when the shower was installed some 30 years ago.

If it is that old, you need to plan a complete redo of materials from the inside of the wall out. Your valves will need replacing, and there is very likely water damage behind the wall. Cedar is rot resistant, but it is not waterproof. It will have allowed moisture behind the walls no matter how it was treated originally.

If there is 30lb. felt behind that cedar, I doubt there is any water damage. Get a $39.00 random orbital sander with an assortment of grits and it will look new in a few hours at most.