Ahh yes - you might want to add
&& $xf.visitor.user_state == 'valid'to the display criteria for menu items and widgets to hide them from users who are not in the valid state.
Note that this will also hide these elements for users from members whose email has bounced or who are waiting for email confirmation after changing their email address.
I've updated the addon to hide the What's New and New Posts buttons from members without a valid user_state and updated the instructions in the tutorial to include the user_state check for various menu items and widgets.
Thanks for bringing this to my attention @xTriz - this is an improvement to the addon and tutorial and I've implemented it on my own sites.