The crinkle finish is rather tough, and should handle soap, water and a soft cloth. I don't know about baking soda, since it's an abrasive, be it a mild on. Clean and in good condition the crinkle finish has shine to it. As leonf mentions, it could be more dirt. I have seen one or two cases were a surface or paint originally hard and shiny has been exposed to some type of oil or grime that over time made it soft and a bit gummy. It's not common with sewing machines I've seen, but I have come across it once or twice.
Your machine looks like a gem and in very nice codition. You can wring up one of those velvety microfiber cloths and choose a spot and clean with swirly movments; if the brown stops rubbing off I'm guessing it's stubborn dirt, but it has to be done carefully and in a not so visible spot. Hard to tell from the pictures. A clear glase or sealant type car polish with out the white gritty polish ingredient will protect and shine up a worn finish, and the finish dries to a very hard film too. The basic resin polish can be hard to polish up and out of all the crinkles, the sealant type works well though.
Last edited by Mickey2; 08-10-2017 at 11:29 AM.