Woodworking is my other hobby. Polyurethane is basically plastic. The waterbased poly is transparent. I am not sure you (or anyone) would be able to tell the difference in sound if the walls were finished with polyurethane vs. oil vs. lacquer vs. shellac. Music instruments are usually finished with lacquer or shellac as it is possible to get the finish very glossy. Here are some pro's and con's to consider for each.
Polyurethane and lacquer are both plastics. I much prefer the look of lacquer over poly. Both the waterbased poly and lacquer dry very quickly allowing multiple coats per day. The poly is the more durable finish being more scratch and water resistant. Both will yellow if exposed to sunlight. Refinishing lacquer is easy as each layer melts into the previous. With poly each layer is individual. Also of note is that the waterbased poly really has a blue tint to it. You will see this when it is sprayed on thickly. So when it dries it gives the walnut more of a "cool" tint (as opposed to warm).
Oil (tung or linseed) -- if you go this route it will darken the wood and give it more warmth. The oil soaks into the wood so there is no "film" on the surface. It is very easily "repairable" -- just scuff sand and recoat. You can only do one coat per day -- wipe it on and let dry. Repeat for 3-4 days. Do not throw the oily rags into a pile or they will start a fire. The product I recommend here is Watco (this is a blend of tung and linseed)
Shellac -- this is a natural product (even used by the Egyptians 1000's of years ago). It is a secretion from the lac bug dissolved in denatured alcohol. Again this dries extremely quickly and allows multiple coats per day. It comes in different shades of amber -- from very light yellowish to dark amber. It looks really good on Walnut. Very easy to repair -- scuff sand and spay more on as again each layer melts into the previous to form one continuous film. You might want to get some and spray it on a board and see what you think. You can buy a spray can at your local box store for $5 or so.
If you go the poly route I like a brand call "General Finishes".
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Also just used pure Tung Oil on my last place for doors, interior walls and ceiling... adds a nice density and on interiors lasts many years.
Once I purchased Vivid speakers with side firing woofers I measured and found that ~1.5DB was being lost through the walls adjacent to the outward facing bass drivers (slightly worse for the inside wall which is hollow). I experimented with MDF untreated and 3/4" Baltic birch with water based poly. There was no audible difference. I'd bet unless you used something highly reverberant like glass you won't be able to hear a difference irrespective of finish or material assuming same shape and size. BTW - the 3/4" Baltic Birch is still in place along the side walls near the out firing woofers and my room is tuned with them in place.
Soap would be a pretty good choice for walls since they don’t endure a lot of contact. Soap works well on furniture but needs re-applied more often on it.