Baking soda is water soluble, and it is quite basic in pH in a water solution. I'd rather use something less chemically active. In time, any potential chemical activity will be actual chemical activity. Sodium bicarbonate is used to "age" wood. To me that means it is reacting with the wood chemically. Typically we would not expect that process to be beneficial where wood preservation is concerned. I would have some concerns about the chemical activity being concentrated on the wooden threads that hold the post in position.
As usual, there are other ways. First we should understand just exactly why the posts have become loose enough to rotate. This is typical of what happens with metal / wood interfaces over many seasons of wood shrinking and expanding against metal which shrinks and expands less. The wood will expand against the metal and being bound, the wood will become compressed under the collar of the post where the post rests on the wood. The compression will reduce the friction that held the post in place and against the strong wire spring pressure, the loosened post will now rotate. What has been lost is the friction of a tight fit, and that friction was acting between the collar of the post and the wood joint surface. The least invasive solution would be to put something in between the post collar and the wood surface that restores the friction.
It would be helpful if this material was more compressible than wood and certainly better if the material is chemically neutral. Wood is primarily cellulose. Cotton thread is also primarily cellulose. Cotton thread is also more compressible than wood and the fibers of the cotton provide the same kind of friction interface as wood. What I do to tighten a loose post is back it out about one turn or less and wind cotton thread around the post between the post collar and the wood surface of the joint. How many windings? As many as it takes to secure the post in the correct alignment when it is tightened down again. This is invisible, involves no adhesives, involves no drilling, no addition of new hardware that is not original to an instrument, and most importantly;- no potential chemical activity. And so far, it has worked every time I have used the procedure to tighten up a post. Try it, you'll like it.
