It's objective in the sense that some types of food and method of preparation are nearly universally unobjectionable, notwithstanding tastes. For example, few people around the world would ever find raw vegetables or vegetables boiled in a soup disgusting, whatever the vegetable or regardless of whether they liked the taste. For example, most Westerns probably wouldn't be able to tolerate, let alone enjoy, bitter gourd soup. But I doubt it would inspire disgust (i.e. revulsion) in many such people.

Disgusting foods tend to strongly correlate with certain types of preparation, like fermentation, involve animals or animal byproducts, exhibit certain kinds of textures (e.g. soft or mushy), or have certain types of odors (e.g. rancid). That's what I meant by cheese being objectively disgusting--all the characteristics of cheese fall into categories that strongly correlate with disgusting foods.

Obviously each person's particular tastes and preferences are highly subjective. But from an anthropological viewpoint we can make some objective classifications because there are near universal qualitative characteristics of foods that various cultures find disgusting.

Some types of disgust are likely strongly innate rather than cultural, but that's beside the point. For example, for all I know Inuit might be much more likely to find simple vegetable preparations disgusting, so that the objective quality of vegetable soups generally being non-disgusting might simply be an artifact of the dispersal of human populations. But that wouldn't make qualitative classifications any less objective. A factor doesn't need to be innate, it just needs to be common.