I would prefer to let the natural fats and oils in the soap penetrate the hard wood.
I have a Victorian mahogany bench, unvarnished, stays outside in all weathers including snow and freezing conditions, looks perfect. I would be more concerned about water finding its way under the varnish and becoming trapped between a hard wood and varnish.
My wooden shaving bowl is from the 1960s, twenty years ago I used a light stain and varnish, it didn't last, I used steel wool to remove what was left and it is still perfect today.
I will call in at DR Harris later today and ask for their experience and advice.