Index: wp-includes/post-template.php
IDEA additional info:
Subsystem: com.intellij.openapi.diff.impl.patch.CharsetEP
<+>UTF-8
===================================================================
--- wp-includes/post-template.php	(revision 76681c40e3e0ea4e88ba42c9f5820ab4aa3fead7)
+++ wp-includes/post-template.php	(revision )
@@ -711,8 +711,12 @@
 		$classes[] = 'no-customize-support';
 	}
 
-	if ( get_background_color() !== get_theme_support( 'custom-background', 'default-color' ) || get_background_image() )
+	if ( current_theme_supports( 'custom-background' ) && (
+			get_background_color() !== get_theme_support( 'custom-background', 'default-color' ) ||
+			get_background_image() )
+	) {
 		$classes[] = 'custom-background';
+	}
 
 	if ( has_custom_logo() ) {
 		$classes[] = 'wp-custom-logo';