I quite frankly question if that is true. A family member is allergic to eggs, as in "he will die if eggs have been near food he consumes". Local bakers have absolutely no issue producing cakes and bread for events when he asks and the prices difference is negligible.
Because they aren't running a production line. And eggs don't make dust.
Produce an item, clean your utensils before the next time. Minimal cross-contamination issues.
A production line processing sesame will create a certain amount of sesame dust. Ensuring that dust gets nowhere near other production equipment is expensive.