How to automatically generate a random url for a views rss feed?
Just configure the menu path for the page/feed display of your view to include a "random" token. You can set them to be whatever you want.

Users will require the token to trigger the menu item and therefore view. You can rotate the token by simply updating the view (though it's a manual process).

If you need to automate rotating the token, you could build a module that hook_menu_alter's  access callbacks (yourmodule_access) onto the desired paths that checks the token (variable_get) that a hook_cron periodically updates (variable_set) and mails out to appropriate admins (users with some role). This has added benefit that it's not limited to use with Views. Though that's a bit complex for providing obscurity.

Also, many RSS readers support HTTP basic auth (via adding username:password@hostname to the feed URL), so you could install a contrib module that adds support for logging in via HTTP Basic.