Loops in category description

What you want to do is to group fruits by color. In WordPress term appropriate mechanism for that is taxonomy (categories and tags are examples of taxonomy).

I would create a custom taxonomy “fruit color” where terms would be individual colors and assigned to fruits.

Then your display logic would be to:

  • retrieve all fruit colors terms
  • for each term display its title and posts that have the term assigned

You could do this with tags (since tags are taxonomy), but it works cleaner when taxonomies have specific purpose and don’t mean different things in different contexts (as in your tag would mean “color” for fruits, but something entirely different for non-fruits).