For many of Britain's dairy-eating days, cheese was yellowy orange because of the beta-Carotene in the grass eaten by cows. This pigment was transferred to the milk and cheese, and the more vibrant the color, the better quality the cheese was presumed to be. After all, you don't want cheese from some sad, underfed cow. But during the 17th century, cheese makers started removing the cream to sell or churn into butter. And because the beta-Carotene was carried in the cream, they were left with low-fat white cheese.
This was centuries before "low-fat" was a selling point, so white cheese was colored with carrot juice and other additives to look like the real deal. That tradition made it to America, and has stuck around. Consumers expect orange cheese, so they get orange cheese. It also worked as a marketing gimmick, helping cheese stand out from competition that decided to go au naturel, because cheese is apparently purchased with the same "Color makes it better!" logic as comic books. The trend didn't catch on everywhere (Vermont is a notable exception), which is why some are still white. And of course, for some cheeses, that's become part of their own image. Bright orange brie would just look weird.
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