The only ingredients in Ben & Jerry's vanilla ice cream that aren't in Haagen Dazs are guar gum (which is a ground bean, and natural enough to be sold in a bag for your kitchen by Bob's Red Mill) and carageenan, which sure, can be considered a derived ingredient but is ultimately derived from seaweed and is almost certainly not the cause of any health issues. Those thickeners are a far cry from industrial concoctions like hydrogenated oils.
I mean, canned soups are on the list an ultra-processed food. Oh no!! I assure you we're not suffering a health crisis due to canned soups in the generic. It's all nonsense.