Does iControl (or any other F5 api) allow anonymous access?

Simple answer, nope.

Hi Charles,

as Brad already said, the REST API requires always authentication.

But you could use a virtual server to reverse proxy the access to the API. By doing this you would be able to insert some low priv Basic credentials on the fly and able to restrict the access to specific calls to make it at least a little bit secure.

Note: If I where you, then I wouldn't do this! ;-)

Cheers, Kai