I was told to bring a dessert that is NOT savory....what would you infer is meant?
Because so many cakes, sweet tarts, and classical sweet desserts can be made with a sprinkle of salt (and this is in the recipes of a lot of sweets) I don't think we are looking at a dessert with no spices nor salt. 

It might be tasteless. 

I'm guessing, without knowing the context, that it meant no onion tart, mushroom bell pepper tart, or prosciutto wrapped fruits etc. 

When sugar was first abundantly available in Europe, a lot of cooks put sugar on everything - meat, stews and so on. There might be something in our food history where desserts, sweet and savory, combined a lot more than today.