Bootstrap dropdown in navbar with AngularJS & Jade

First it would be best to move the ng-click expressions and find them a safe home in this views Controller. ng-init is only needed in very specific cases plus it clutters up your DOM.

$scope.isCollapsed = true;

$scope.toggleCollapseState = function($event) {
  $scope.isCollapsed = !$scope.isCollapsed;
}

// DOM
button.navbar-toggle(type='button', ng-click='toggleCollapseState')

In regards to your toggling issue. It appears that there is a ng-click attribute which accepts an expression (in this case you want to use a function) that you can attach to the element that has uib-dropdown-toggle on it.

li(uib-dropdown=true,dropdown-append-to-body=false)
  a(href=true,uib-dropdown-toggle=true ng-click='navListDropdownToggled') Dropdown

You can then take the $event local that ng-click passes to the expression to stop propagation to the parent element(s).

$scope.navListDropdownToggled = function navListDropdownToggledFn($event) {
  $event.stopPropagation();

  // If you need to handle any toggle state-based logic 
  // you can do it by altering the isCollapsed variable.
  // $scope.isCollapsed = true;  
} 

EDIT:

According to Bootstraps Documentation, there is also an on-toggle attribute that passes the $event local as well, so this could be a more appropriate replacement for the ng-click.