There's no such thing as naturally orange cheese.
Back in the 17th century, when cows were grass-fed grazers, beta-carotenes from the grass would work their way into the cheese giving it a “natural yellowish-orange pigment.” This soft orange glow was a sign of a good, rich, full-fat cheese.
Over the winter, they ate hay, which is dried grass. It had lost the beta carotenes, so the milk was paler.
Also, cheese producers looking to up their profits would often skim the cream from the cheese to sell separately and would lose the orange tint (& be lower quality).
Perception is everything:
People saw the yellower cheese as being better. So, cheese makers made up for it by dying the cheese with annatto (dye made from achiote seeds) to make it look more like cheese from well-fed cows, and get a higher price for it.
Then, in a cheese maker's arms race, more colour was considered better until it ended up orange.
While this tradition continues today, cheese makers (particularly of cheddar) now use less natural dyes to get this orange colour, and you end up ingesting unnecessary chemicals.
If you are a cheddar lover, you have options. As always, a good rule of thumb is to buy the shortest ingredient list. Cheddar with 3 ingredients or less does not contain colouring. And if all else fails, at least search for those colored with (all-natural) Annatto. And, of course, the easiest solution? Buy white cheese. ☺️