Steps to reproduce the issue

1. Have a menu item that has at least two items, one with public access, one with any of the other (registered) access types. (I'll use registered for this example)
2. Have a login module that redirects to the homepage after logout.
3. Login as a registered user. (You'll see the restricted menu item)
4. Logout

Expected result

The registered access menu item should not be visible

Actual result

The registered access menu item remains visible until page refresh

System information (as much as possible)

updated 3.5.1 to 3.6

Additional comments

The login module redirect is actually not required to reproduce this but makes it even more compelling, since the redirect itself causes an inherent reload of the page.