Yes, you should definitely leave the salt out of the recipe, but the cake may still taste too salty depending on your butter, and your tastebuds. Salted butter varies a lot in how much salt it contains.
I don’t have my Bible with me now, but most of her cake recipes, like her Favorite Yellow Layer Cake, only have 1/4 teaspoon or so salt.
I have read that there can be up to 3% salt in salted butter, or about 3/4 teaspoon salt per stick of butter. If the recipe calls for 2 sticks of softened butter, and your salted butter is on the salty side, the cake might suffer as it would be easily quadruple the salt level called for in the recipe.
Whether you can substitute salted butter for unsalted. I think it depends on how much salt is in the recipe, and what type of finished product. I think cakes, especially white cakes, have a more delicate flavor and texture, and I would avoid the salted butter. However, for cookies or bread, or something with a lot of chocolate or caramel or nuts, I don’t worry too much about the substitution, and usually just leave the salt out of the recipe.