Again, it depends on the definitions; "internet security" is very well achievable; it is mostly based on what is your "internet"

My definition of internet is the hosts reachable via routable IP protocol family. It is pretty easy to arrange the routing so that the originating host is hidden from both the target host and any given intermediate host. (that's called onion routing, btw )

On the other hand, if your definition of internet is connection to some service that you need to authenticate to use, then of course there is no way you can remain anonymous. (this encompasses almost all social media or messenger-type applications)