Reasonably sterile. The pool and the shower water has chlorine in it (bleach sterilizes things) and most of us close our eyes when shampooing. 
The idea isn’t that all possible contaminants have to be kept from the eye. The idea is that you don’t want bacteria growing in the eye drops, because while some contaminants won’t hurt your eye, others will blind you.
This right here is what needs to stop. The US is subsidizing the rest of the world’s medication. Easy solution - drug companies can’t charge us any more than they charge Europe or Canada. That would force price hikes in those countries, which would allow them to bring our costs down.