I had a problem with the background of BottomNavigationView when pressing menu. It only happened when I set fontFamily. You can see the demo below, it always shows the white background for a light theme and black for a dark theme.
For the version material design 1.1.0-alpha05 it hadn't this problem.
Tested on Android 9.0
Material design version: 1.1.0-alpha08
<style name="Widget.BottomNavigationView" parent="Widget.MaterialComponents.BottomNavigationView">
<item name="android:fontFamily">@font/roboto_condensed_bold</item>
<item name="fontFamily">@font/roboto_condensed_bold</item>
</style>
<com.google.android.material.bottomnavigation.BottomNavigationView
android:id="@+id/bottomNavigationView"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_gravity="bottom"
android:layout_marginEnd="0dp"
android:layout_marginStart="0dp"
android:theme="@style/Widget.BottomNavigationView"
app:menu="@menu/navigation" />

When don't use fontFamily

If I set global fontFamily for the app's theme then this problem can resolve but I don't want to use same a font for all views.
Have you tried changing this
android:theme="@style/Widget.BottomNavigationView"
for
style="@style/Widget.BottomNavigationView"
and also the property name is twice in your style, this should be enough:
<item name="fontFamily">@font/roboto_condensed_bold</item>
@GuanacoDevs Before I tried your way. Using style will not work with BottomNavigationView
I fixed workaround use itemTextAppearanceActive/InActivate.
<style name="Widget.BottomNavigationView" parent="Widget.MaterialComponents.BottomNavigationView">
<item name="itemTextAppearanceActive">@style/BottomNavigationTextActivate</item>
<item name="itemTextAppearanceInactive">@style/BottomNavigationTextInactivate</item>
</style>
<style name="BottomNavigationTextActivate">
<item name="fontFamily">@font/roboto_condensed_bold</item>
<item name="android:textSize">12sp</item> <!-- Disable the zoom animation when switch tab -->
</style>
<style name="BottomNavigationTextInactivate" parent="BottomNavigationTextActivate" />
and use style instead of android:theme
<com.google.android.material.bottomnavigation.BottomNavigationView
android:id="@+id/bottomNavigationView"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_gravity="bottom"
android:layout_marginEnd="0dp"
android:layout_marginStart="0dp"
style="@style/Widget.BottomNavigationView"
app:menu="@menu/navigation" />
Most helpful comment
I fixed workaround use itemTextAppearanceActive/InActivate.
and use style instead of android:theme