I definitely couldn't play with a friend like that.
When I play with my friend we'll share resources, because we pretty much always go on an adventure together to gather it up anyway (What's the point spelunkering and gathering on your own, if playing with a friend? You might as well play singleplayer). If we want to make something we'll ask the other if we can. And if there are limited resources, then we only make the items neccesarry for us to carry on, for example, we'd always upgrade someone to a new pickaxe tier before one of us upgrading a helmet, so we can both benefit from it's creation.
Besides the Wood tier armous we always tend to set out who is going to have what in advance anyway, so one of us will set up to get, say Crimtane Armour, while the other might go for Meteorite.
That way we know we're not going to be fighting for the resources, and it won't end up with us wearing mismatched pieces of armour, so we can get the respective bonuses for having complete sets.