Final answer:
The website OPNAVIST contains a listing of all the current OPNAV sensitive directives. There is no publicly accessible website that provides a listing of all the current classified directives.
Step-by-step explanation:
The website that contains a listing of all the current OPNAV sensitive directives is OPNAVIST. It is the official website of the United States Navy that provides information on policies, directives, and instructions issued by the Office of the Chief of Naval Operations (OPNAV). You can find a comprehensive list of all the current OPNAV sensitive directives on this website.
As for the listing of all the current classified directives, there is no publicly accessible website that provides such information. Classified directives contain sensitive and confidential information that is not available to the general public. Access to classified information is restricted to authorized personnel with proper security clearances.