This is my take on kosher diet coke.

If you read the Cane Sugar Dr. Pepper threads you'll see that in some areas cans are marked "sugar and/or cane syrup". In some cases the bottler switches sweeteners and there is what I'd call friendly contamination. They don't clean the cane sugar out completely when switching from a sugar drink to a corn syrup drink and you get a mix until all the sugar crystals wash away into the new syrup.

I'm assuming the kosher diet coke is in the same thought as "this chocolate is processed in a facility that also processes peanuts".

They are just warning you that some of the other ingredient might make it into what you are consuming.

In the case of diet coke it shouldn't have cane sugar in it but if it does it's still kosher. The kosher label just assures you that it won't have corn syrup not that it won't have sugar.

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I have 12 packs in my fridge, closet, trunk, and occasionally in random locations.