This is a major topic in and of itself. Briefly, there are 2 major theories. One being that every common wood finish will EVENTUALLY be safe for food contact given enough time for the solvents and other nasties to evaporate/bind/or otherwise become inert enough to not harm. The other theory is that that is a bunch of BS and you can only use immediately natural foodsafe ingredients to be truely safe.
The proponents of the "everything is foodsafe eventually" idea tend to only concentrate on the solvents used in those finishes. There's more to it than just solvents, you know. They also tend to cite (or, more accurately, cite a common finishing article-writer) the notion that nothing in most of these finishes are listed as a health concern with the American USDA. Of course, lead wasn't listed for many many years before its effects were known either. This is only one example out of thousands.
Personally, I'm in the middle. If I'm making something (like my kitchenware) that I'm going to sell or send to my retailers relatively soon, then I'm going to use natural oils, waxes, etc. because I don't want to have to hold on to them for MYSELF feeling safe. If I have something that I can hold onto for awhile (again, long enough for me to feel like it's safe) then I MIGHT use some other finish IF that finish is the best for the piece given what it's going to be used for, etc.
I also don't take product labeling or advertising at face value either. Many so-called "Salad Bowl Finishes" have solvents and other ingredients in them that I don't consider immediately food-safe. In fact, a couple of these products have changed their labeling recently to reflect their, let's just say creative marketing ideas. They've changed them to read something like "Food Safe after 30 days".
As for your question about applied finish over dyes/stains, as long as your dye/stain doesn't have ingredients that could leech out/under/over/around the finish, then you're safe. Just because you put a finish over something doesn't mean that what is under it stays under it. It depends on many factors.
- Andrew