Why? First, finger oils shorten the life of the strings. Secondly, rosin dust sinks into the varnish, bringing with it a lot of dirt and dust. This not only looks ugly, but it will eventually choke the sound of the instrument. It is very easy to simply wipe the strings and instrument before putting it away in its case.
If the instrument is very dirty, a damp cloth will do a good job of cleaning. Be patient; this will take awhile. The use of solvents or chemical polish is not recommended because of the danger of damaging the finish or rendering a crack or seam unglued.