In a lot of food serving/producing establishments - it's actually considered a health hazard. Your nose ring falls out into the drinks and, well...... it's a physical hazard (since you can choke on it), and a microbial hazard (since it was in contact with the wearer).
When I worked for Starbucks that is what they told me (well not as fancy, just that it could fall in the beverages).
Now I work for a big beef producer here in Canada and it's the same reason. And for that reason, it makes sense. If you can't take it out, you can't be in the plant.