diff --git a/core/lib/Drupal/Core/Theme/Registry.php b/core/lib/Drupal/Core/Theme/Registry.php
index cb9fe42..317bada 100644
--- a/core/lib/Drupal/Core/Theme/Registry.php
+++ b/core/lib/Drupal/Core/Theme/Registry.php
@@ -456,12 +456,14 @@ protected function processExtension(array &$cache, $name, $type, $theme, $path)
         // A template file is the default implementation for a theme hook, but
         // if the theme hook specifies a function callback instead, check to
         // ensure the function actually exists.
-        if (isset($info['function']) && !function_exists($info['function'])) {
-          throw new \BadFunctionCallException(sprintf(
-            'Theme hook "%s" refers to a theme function callback that does not exist: "%s"',
-            $hook,
-            $info['function']
-          ));
+        if (isset($info['function'])) {
+          if (!function_exists($info['function'])) {
+            throw new \BadFunctionCallException(sprintf(
+                'Theme hook "%s" refers to a theme function callback that does not exist: "%s"',
+                $hook,
+                $info['function']
+              ));
+          }
         }
         // Provide a default naming convention for 'template' based on the
         // hook used. If the template does not exist, the theme engine used
@@ -490,11 +492,8 @@ protected function processExtension(array &$cache, $name, $type, $theme, $path)
           $info['preprocess functions'] = array();
           $prefixes = array();
           if ($type == 'module') {
-            // Add template preprocessor only for templates.
-            if (!isset($info['function'])) {
-              // Default variable preprocessor prefix.
-              $prefixes[] = 'template';
-            }
+            // Default variable preprocessor prefix.
+            $prefixes[] = 'template';
             // Add all modules so they can intervene with their own variable
             // preprocessors. This allows them to provide variable preprocessors
             // even if they are not the owner of the current hook.