Any of the washed-curd types (washed early in the make process) will get you there - Gouda, Edam, Havarti, Butterkase, etc. Plus the texture is probably the closest of a "real" cheese to an American (Processed) Cheese, which could be the norm for some folks. Colby- and Jack-types, washed later in the process (after some acidification in the vat) are also mild but with more hints of cheddar-type flavor.
Its also hard to know what someone means by "sharp", as it seems to be the only way to describe cheese that some people know. For some "sharp" means full and complex flavors, for some it means the tang of acidity, and so on. It can be hard to pinpoint what someone finds disagreeable about a certain style.