create a color directory in res folder and create your xml file for customize your bottom navigation items:
res/color/bottom_nav_color.xml:
<?xml version="1.0" encoding="utf-8"?>
<selector xmlns:android="http://schemas.android.com/apk/res/android">
<item android:state_checked="true" android:color="@color/your_color" />
<item android:state_checked="false" android:color="@color/your_color"/>
</selector>
and in your BottomNavigationView set app:itemTextColor and app:itemIconTint values to @color/bottom_nav_color
<android.support.design.widget.BottomNavigationView
xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
android:id="@+id/main_navigation"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_alignParentBottom="true"
android:background="@color/actionBarColor"
app:menu="@menu/my_navigation_items"
app:itemTextColor="@color/bottom_nav_color"
app:itemIconTint="@color/bottom_nav_color"/>