My relatives, when buying a bread, do not look at ingredients. I know that sometimes there is margarine there: local muslim community marked margarine as doubtful component, which can be derived from prohibited animal (I'm also absolutely sure that relatives do not try to do any investigation about this ingredient). And as they don't think of bread as smth. dirty, quite often plates, knifes are not washed after it. So it easily can go to halal meals. May I eat such meals (sometimes I see how bread crumbs go to meals, but usually I'm unaware about it)? Also if plate/knife/spoon of my relative goes in contact with halal meal, cooked by myself, may I still eat it? May I eat such meals if by not eating them, I can cause fitna?
Meat is the only thing you need to investigate. You have too feel sure that it is Halaal. You may never eat haram meat unless you are under the threat to life or limb if you do not.
With things like margarine and bread, you are allowed to eat without investigation. However, if you know (not merely suspect) that there is haram animal fat in a particular piece of bread or in margarin, then you cannot eat from it, not even a crumb.