How to remove "starred" tab in gnome's nautilus?

Unfortunately the auto-detection of whether to show the 'Starred' panel based on whether you have any starred items was decided against. I don't know why it is shown even without Tracker being available, though.

Note that the sidebar is actually a single unit provided by Gtk, not an editable collection of random items – but still sufficiently customizable for this purpose.

Option 1: Override the built-in UI description.

1. Create a location for the overrides:

   mkdir ~/.config/nautilus/ui
   

2. Extract the resource description of the main window:

   gresource extract /bin/nautilus \
             /org/gnome/nautilus/ui/nautilus-window.ui \
             > ~/.config/nautilus/ui/nautilus-window.ui
   

3. Edit the properties of the GtkPlacesSidebar object:

   <object class="GtkPlacesSidebar" id="places_sidebar">
     ...
     <property name="show-recent">False</property>
     <property name="show-starred-location">False</property>
     ...
   </object>
   

4. Set the environment variable to make GLib use this override:

   export G_RESOURCE_OVERLAYS="/org/gnome/nautilus/ui=$HOME/.config/nautilus/ui"
   

   Due to Nautilus being started via D-Bus, you will likely need to set this via ~/.pam_environment…

   G_RESOURCE_OVERLAYS DEFAULT="/org/gnome/nautilus/ui=/home/confetti/.config/nautilus/ui"
   

   …or via ~/.config/systemd/user/dbus.service.d/environment.conf:

   [Service]
   Environment="G_RESOURCE_OVERLAYS=/org/gnome/nautilus/ui=/home/confetti/.config/nautilus/ui"
   

Option 2: Recompile Nautilus with this patch applied:

diff --git a/src/nautilus-window.c b/src/nautilus-window.c
index 0d1234f15..7a6d567f6 100644
--- a/src/nautilus-window.c
+++ b/src/nautilus-window.c
@@ -1347,6 +1347,12 @@ nautilus_window_set_up_sidebar (NautilusWindow *window)
                                         | GTK_PLACES_OPEN_NEW_TAB
                                         | GTK_PLACES_OPEN_NEW_WINDOW));

+    gtk_places_sidebar_set_show_recent (GTK_PLACES_SIDEBAR (window->places_sidebar),
+                                        FALSE);
+
+    gtk_places_sidebar_set_show_starred_location (GTK_PLACES_SIDEBAR (window->places_sidebar),
+                                                  FALSE);
+
     g_signal_connect_swapped (window->places_sidebar, "open-location",
                               G_CALLBACK (open_location_cb), window);
     g_signal_connect (window->places_sidebar, "show-error-message",

To the second part of your question. To remove the "Recent" tab, run this command under your user:

$ gsettings set org.gnome.desktop.privacy remember-recent-files false

Alas, I can't find the similar command for the "Starred" tab.