Can you eat cheddar when you are breast feeding?

Yes
It's safe to eat whilst you're breast feeding, though it can affect you it is unlikely to affect your baby.
Cheddar cheese is a relatively hard, pale yellow to off-white (unless artificially coloured), and sometimes sharp-tasting, cheese. Originating in the English village of Cheddar in Somerset, cheeses of this style are produced beyond this region and in several countries around the world.
Granular cheese, also known as stirred curd cheese and hard cheese, is a type of cheese produced by repeatedly stirring and draining a mixture of curd and whey. It can refer to a wide variety of cheeses, including the grana cheeses such as Parmigiano-Reggiano (at right) and various others. Many types are commonly used in the production of processed cheese, especially American cheese, which by law must consist of Cheddar cheese, Colby cheese, cheese curd, or granular cheese.