Perhaps the difference in serving new vs. opened items is whether the item may have been touched by a serving implement, and therefore runs the risk of "contamination"? Milk, ketchup, and salad dressings come straight out of the container onto the food or into the glass. Ice cream pretty much has to be scooped/touched, and to a lesser extent things like chips can be scooped out by hand so it's harder to prove that it hasn't been ... germed up, for lack of a better expression. Butter/spreads are kind of a mixed bag - you need a serving implement but far fewer people are likely to lick the butter knife.
I'm not generally bothered by germs myself - I don't notice things like double-dipping and I have no issues using my hand to get food that other people use their hands on (bowls of chips, nuts, etc). Typical exception to this is seeing small children manhandle items or dig around in a bowl or bag. I won't eat any of it after that. Extraordinary exception was seeing an adult serving slices from a large sheet cake and using fingers and knife to transfer slices to plates, while absently licking her fingers between slices. That was just egregious.
But personally, I'm not comfortable serving or being served anything that smacks of being a remnant, like with less than half-full bottles of salad dressing or mostly empty bags of chips. So for me, it's not whether the ice cream box/tub was new or not-new, it's whether it was fresh, even if partially gone, or not-fresh.
