Regular read user:
I get why they wouldn't have any way to edit anything, but how come they don't see the quick launch or the doc lib web part? What can they see / do?
thats because anonymous uses are still based on limmited access.
have you disabled -> "limmited-access user permission lockdown mode" its a feature within sitecollection that is enabled by default. That should solve your issue.
if its still an issue follow this simple guide to setting up anonymous access to your site collection.... its a few areas that you need to change if you havent already!