While centuries ago, that yellow-orange hue of cheddar was a natural occurrence due to the beta-carotene-rich diet of dairy cows, the current batches of cheddar are simply dyed.
Annatto, a natural dye extracted from achiote seeds, is popularly used to give cheddar its orange color, with alternative options including paprika or artificial colorants.
However, this practice of dyeing does not impact the flavor of cheddar and is solely an aesthetic choice. Moreover, there’s no other difference between orange and white cheddar.
It’s worth noting that the dyes utilized in cheddar have undergone safety testing. Therefore, if you prefer the orange variety over the white one, there’s no cause for concern.