Why would you want anon's to post to your SharePoint site?
It's a good wya to oveload your server with SPAM

I've had several clients with valid reasons for wanting to collect
information from anonymous users. Using InfoPath makes it possible to put
validation code in the form that would cut down on the amount of spam
produced. There are lots of reasons, it just isn't possible given the way
SharePoint does anonymous access.

You could add a CAPTCHA or similar human-verifiable test like math equations or
asking an obtuse question like, "What is the name of the guy on first base?"

To which the correct answer is "no".