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I added a FloatingActionButton in the layout where its only parent is a CoordinatorLayout, so I don't understand where the backgroundTint color is coming from.

I tried to change the color to match the inner circle, but it changes the whole button to a solid color.

I also applied a different style, but it does not change the button at all.
I fixed this problem in the past, but I don't remember how I did it.

<android.support.design.widget.FloatingActionButton
 android:id="@+id/fab"
 android:layout_width="wrap_content"
 android:layout_height="wrap_content"
 android:layout_margin="16dp"
 android:src="@drawable/ic_action_add"
 app:layout_anchor="@+id/edit_layout"
 app:layout_anchorGravity="bottom|right|end" />

The gray color comes from your colorAccent defined for the app theme in style.xml. Now the @drawable/ic_action_add is a plus sign inside a filled circle. Try to use below icon instead:

ic_add_black_24dp.xml

<vector xmlns:android="http://schemas.android.com/apk/res/android"
 android:width="24dp"
 android:height="24dp"
 android:viewportWidth="24.0"
 android:viewportHeight="24.0">
 <path
 android:fillColor="#000000"
 android:pathData="M19,13h-6v6h-2v-6H5v-2h6V5h2v6h6v2z" />
</vector>

Then set a crimson color to the FloatingActionButton's background tint and the gray one for icon tint:

<android.support.design.widget.FloatingActionButton
 android:id="@+id/fab"
 android:layout_width="wrap_content"
 android:layout_height="wrap_content"
 android:layout_gravity="bottom|end"
 android:layout_margin="16dp"
 app:layout_anchor="@+id/edit_layout"
 app:layout_anchorGravity="bottom|right|end"
 app:tint="#404D54"
 app:backgroundTint="#6F303A"
 app:srcCompat="@drawable/ic_add_black_24dp" />

Result:

You are not providing any app:backgroundTint, so it is using the default colorAccent from colors.xml.

To solve this:

1.Add a new color to colors.xml

<color name="fab_tint">#33d1ac</color>

2.Change the code as follows:

 <android.support.design.widget.FloatingActionButton
 android:id="@+id/fab"
 android:layout_width="wrap_content"
 android:layout_height="wrap_content"
 android:layout_margin="16dp"
 android:src="@drawable/ic_action_add"
 app:layout_anchor="@+id/edit_layout"
 app:layout_anchorGravity="bottom|right|end" 
 app:backgroundTint="@color/fab_tint"/>