I'd argue that unsecured HTTP (e.g. no authentication in place and on the public internet) is akin to trespassing on unsecured property, or entering an unlocked door. Entering a secured system without authorization (e.g. through some hack, social engineering, etc) would be more like breaking and entering.
I understand the distinction you're making, implicitly, between entering virtual space and physical space, but stand by my analogy.
Unsecured systems (HTTP or otherwise) are like doors left open, and secured systems are like locked doors. It should be, I argue, left to the possessor of the space (e.g. physical place or network host) to determine whether access is (or was) acceptable.
There are standards in some localities surrounding posting notices of "No Trespassing" to indicate private space that is not open to the public (even if it is not physically restricted, such as with a fence or wall). Perhaps a similar requirement would be suitable in these cases, and without such, hosts of unsecured HTTP sites might then have no right to "cry when somebody reads it".