UPDATE: Please note that I'm using the Helix 2 Framework on my site, and in order to fix this issue temporarily, and be able to actually hide my menus (without un-publishing the item, so people can still see the page IF they have the URL, but can no longer browse the page via the menu) I applied a custom CSS class called "hidden" to the menu item (under the "Helix Megamenu options").

The CSS class is
.hidden {display: none !important;} /* For hiding any elements you don't want to see */

Once this class is applied on the backend under the Helix options, the item no longer shows on my menu.

Yet, I would prefer to simply use Joomla's 3.5.1 new feature, an not apply this CSS class.

See screenshot for reference.

Just realized that adding this "custom class" via Helix 2 framework, also applied the CSS class to the tag of the actual pages, and thus all my content on each hidden menu item's related page (article) was also hidden...

Thus, I had to remove this "hidden" class, and I'm back to square one (trying to figure out how to "hide" some menu items, without un-publishing, and without any other methods).

This is a problem with the helix framework and not a problem with joomla.

I am closing this as it is not an issue with Joomla but with the Helix framework and you should report the issue to the makers of Helix

Thanks for letting me know :-)