I have driven past this so many times, and finally stopped today. I took a chance and tried one of their flavors in a tub, Tuffy’s Toffee. Thus far, I’ve had no issues with it. I did see the pre-packaged afterwards, so bought 2 individual containers of vanilla and strawberry. They had a sign indicating that those are recommended for those with allergies.
If you can't handle stick to the pre-packed pints & cups. The vanilla, chocolate, and strawberry only have milk as an allergen. I get the pre-packed pints and have never gotten sick and long as I avoid the flavors with wheat.
The scooped area and milkshakes have cross contact issues, so avoid those if you need to.