I have the product set to Shipping Exempt and the weight set to zero, screen shot: https://www.floridasbestfruit.com/working/201229/ProductSettings.jpg
Yet when purchasing it still charges the shipping minimum, screen shot: https://www.floridasbestfruit.com/working/201229/PublicView.jpg
Check the product option - Do you have a weight set there, and is it an "alt" product option. If so, check that that item does not have a weight assigned.