Wood ash contains large concentrations of potassium salts
which are alkaliine in reaction. If the soil contains high
levels of organic material, it will tend to be acidic and
could tolerate moderate amounts of ash without any real problem.
If, however, the soil is short on organic and/or essentially
neutral or alkaline in reaction, adding wood ash to the soil
would jack up the pH to problem levels.
Bottom line . . . a little bit of ash may be O.K. in some
soils but otherwise, don't.