Yes, I will always open/buy a new container and would prefer that others do the same. This is because while I know I and other members of my household don't eat directly out of ice cream containers with our used spoons, I realize that other people have no way of knowing that. Therefore, I want to allay any concerns guests might have about that.
I'll also say that, with a certain family of relatives I have, it might not even matter if they open a new container. I know that they eat directly out of containers and drink out of bottles and put them back in the fridge, etc. So, I definitely don't eat or drink anything from an opened container in their home.
But I've also seen the mother repeatedly eat off of serving/mixing spoons while dishing stuff up at her parties. So unless I get the very first serving of ice cream or whatever out of a new container with an obviously clean spoon, or can watch her every move while she's plating things, I just stick to eating rolls and a bit of meat or something at their house.
A store bought cake might be okay there, but if it's homemade, she and/or her kids have likely licked the knife/spatula repeatedly while icing it.