How to set the background color of Tab.Navigator?

You need to add the backgroundColor in screenOptions. https://reactnavigation.org/docs/bottom-tab-navigator/#screenoptions Try this:

<Tab.Navigator screenOptions={{
    tabBarOptions: {
        style: {
            backgroundColor: '#f9f9f9',
        },
    },
}}>

in the react-navigation V5 your can to do this:

 <Tab.Navigator
    initialRouteName={'Critic'}
    tabBarOptions={{
       activeTintColor: '#fff',
       inactiveTintColor: 'lightgray',
       activeBackgroundColor: '#c4461c',
       inactiveBackgroundColor: '#b55031',
           style: {
                 backgroundColor: '#CE4418',
                 paddingBottom: 3
           }
    }}
>
    <Tab.Screen name="Critic" component={Critic} options={CriticOptions} />
    <Tab.Screen name="Urgent" component={Urgent} options={UrgentOptions} />
    <Tab.Screen name="Moderate" component={Moderate} options={ModerateOptions} />
    <Tab.Screen name="All" component={All} options={AllOptions} />
 </Tab.Navigator>
);

In React Navigation 6.x, you use tabBarStyle

<Tab.Navigator
  screenOptions={({ route }) => ({
    headerShown: false,
    tabBarStyle: {
      height: 90,
      paddingHorizontal: 5,
      paddingTop: 0,
      backgroundColor: 'rgba(34,36,40,1)',
      position: 'absolute',
      borderTopWidth: 0,
  },
})}
  >
  <Tab.Screen name="Home" component={Home} />
  <Tab.Screen name="List" component={RegistrationList} />
  <Tab.Screen name="News" component={News} />
  <Tab.Screen name="Profile" component={Profile} />
</Tab.Navigator>

Refer documentation here, You need to use barStyle.

Try

<Tab.Navigator
        initialRouteName="Feed"
        shifting={true}
        labeled={false}
        sceneAnimationEnabled={false}
        activeColor="#00aea2"
        inactiveColor="#95a5a6"
        barStyle={{ backgroundColor: '#ffff' }}