How do I change the color of the underline of the active editor tab?

In your scheme .xml file for your IDE settings, try adding:

<option name="TAB_UNDERLINE" value="FFC0CB"/>

in <colors> element.

Programmaticly, this works:

EditorColorsManager.getInstance().getGlobalScheme().setColor(EditorColors.TAB_UNDERLINE, JBColor.PINK);

That unfortunately didn't work.

After digging into the problem a little further, I discovered that the "Accent Color" from the Material UI theme is overriding this value.   Is there a way to make the IDE use the color from TAB_UNDERLINE instead of whatever Material UI is doing?

Here's what my settings look like for a copy of Darcula that has Tab color modified:

<scheme name="_@user_Darcula" version="142" parent_scheme="Darcula">
<metaInfo>
<property name="created">2020-04-11T15:14:56</property>
<property name="ide">Idea</property>
<property name="ideVersion">2020.1.0.0</property>
<property name="modified">2020-04-11T16:01:53</property>
<property name="originalScheme">Darcula</property>
</metaInfo>
<colors>
<option name="TAB_UNDERLINE" value="77008c" />
</colors>
</scheme>

To change the color manually in the IDE, you can do File > Settings > Editor > Color Scheme > General > Tabs > Underline.