When I push a
CNContactViewController *controller = [CNContactViewController viewControllerForUnknownContact:person];
controller.contactStore = [[CNContactStore alloc] init];
controller.delegate = self;
controller.allowsActions = NO;
[self.navigationController pushViewController:controller animated:YES];
Your second screen shot shows the reason for this problem: you have set the tint color for your bar (or bar button items in general) to be white. Hence, they are white in front of the transparent navigation bar and white background in the contact view controller.
You can't do anything directly about the bar tint color, but you can solve this in either of two ways:
One is to make your navigation bar nontranslucent. In that case, the contact view controller's navigation bar will be black, and your white bar button items will be visible.
Another approach is to change your navigation bar's tint color (not the bar tint color, but the tint color that it communicates down to its bar button items) as the contact view controller pushes, and change it back when it pops.
EDIT Okay, I see that there's a further problem because the New Contact view controller is a further view controller presented in front of yours. If you refuse to give up your white bar button item setting, you will have to use the appearance proxy to set the UIBarButtonItem tint color to something else when your push the contact view controller, and then reset it back to your white when your navigation controller delegate tells you that the user is popping back to your view controller.