Despite some similarities, pony foals are definently not like human babies. They can hold their head up from birth and start to crawl/roll around after just a few days; learning to walk properly and saying their first words happens after only a month or two. They also have very large and developed muzzles compare to human infantstheir sense of smell is great and one way they use to identify their familiy. They also start teething very early, and have a full set of teeth even before they are completely weaned (To the discomfort of mothers everywherebottle feeding is very popular in equestria).
What I'm getting at is, pony parents have abolutely no problem doing things which would never work on a human baby -like putting fake nose-tags of their teething infants to stop them putting dangerous things in their mouth. Or to stop them trying to chew through their twin's ears. You were cute when they tried to nurse on each others ears as (toothless) newborns, but it really has to stop before you give each other tetanus or something!
Don't worry, as I said, the tags work the same way fake nose-rings does, and are made from relatively soft rubber-like material. And Applebloom and Pipsqueak only put them on when Cameo and Maria won't stop trying to use each other as teething toys; it's either keeping them separateted from each other (which makes them upset) or the nose-tags, and luckily neither seem to mind them, just being confused/trying to chew on them.