I guess millions of violins have been made without any finish on the inside so it's not that important, but with a little knowledge of wood from my days as a cabinet maker and 25 years in wood products manufacturing, I know it's important to balance both sides of the wood, or a panel, with similar coatings. Wood acts like a living material relative to the absorption of moisture. If you take a 4'x8' wood panel as an extreme example to a violin top, and put laminate or even paint one side, it will bow or cup if the humidity changes as the un-coated side will take on moisture at a faster rate. For a violin, the movement will be slight of course, and the fact that it's basically a beautiful torsion box further keeps you form noticing it or having to worry about. So from my experience, I like the idea of a light coat of oil or sealer to help equalize the absorption of moisture, but again, obviously it's not necessary and there could be some drawbacks if repairs are needed, not sure about how a sealer would affect the woods ability to vibrate as I've also read the theory that the oil varnishes given the wood some flexibility compared to modern varnishes or lacquers. The best example I can give of wood moving is for a traditional style dinning table with "breadboard: ends. This is where the ends of the table, have a edge piece that runs perpendicular to the long boards that make up the table so you don't have end grain exposed at the long ends of the table top. Wood basically only moves across the grain, so as the wood that runs the length of the top moves in width, the end pieces are static so to speak, so the end pieces are fixed only in the middle, and the other attachment points where you have the opposing grain directions, are slotted so the wood can move from season to season. When I made tables like this, the wood was acclimated to my shop, and because I knew the top would move dependent on the seasons and the homes air control systems, I'd tell the client that they can expect to seen the wood move and at times of the year the boards would extend past the edge of the end boards, and at other times they would be short. I remember seeing a client years later, and she told me that her children were always fascinated to see how the wood moved through out the year, and they checked it regularly to see the changes. I used to use the rule of thumb that wood would or could move 1/8" over a 2' width in a modern home with central air. Like it or not, relatively speaking your violin is doing the same thing unless the humidity never changes. Sorry, got carried away, so in principle, finishing on both sides would slow the absorption of moisture and allow it to do so equally so at least it would move in a natural way, not forcing tension between the surfaces which causes unnatural tensions and would stress the glue joints more.