diff --git a/src/wp-includes/class-wp-customize-manager.php b/src/wp-includes/class-wp-customize-manager.php
index 7aa50f7862..81be17b79d 100644
--- a/src/wp-includes/class-wp-customize-manager.php
+++ b/src/wp-includes/class-wp-customize-manager.php
@@ -2885,10 +2885,20 @@ final class WP_Customize_Manager {
 		$this->store_changeset_revision = $allow_revision;
 		add_filter( 'wp_save_post_revision_post_has_changed', array( $this, '_filter_revision_post_has_changed' ), 5, 3 );
 
-		// Update the changeset post. The publish_customize_changeset action will cause the settings in the changeset to be saved via WP_Customize_Setting::save().
+		/*
+		 * Update the changeset post. The publish_customize_changeset action
+		 * will cause the settings in the changeset to be saved via
+		 * WP_Customize_Setting::save().
+		 */
+
+		// Prevent content filters from corrupting JSON in post_content.
 		$has_kses = ( false !== has_filter( 'content_save_pre', 'wp_filter_post_kses' ) );
 		if ( $has_kses ) {
-			kses_remove_filters(); // Prevent KSES from corrupting JSON in post_content.
+			kses_remove_filters();
+		}
+		$has_targeted_link_rel_filters = ( false !== has_filter( 'content_save_pre', 'wp_targeted_link_rel' ) );
+		if ( $has_targeted_link_rel_filters ) {
+			wp_remove_targeted_link_rel_filters();
 		}
 
 		// Note that updating a post with publish status will trigger WP_Customize_Manager::publish_changeset_values().
@@ -2918,9 +2928,15 @@ final class WP_Customize_Manager {
 				$this->_changeset_post_id = $r; // Update cached post ID for the loaded changeset.
 			}
 		}
+
+		// Restore removed content filters.
 		if ( $has_kses ) {
 			kses_init_filters();
 		}
+		if ( $has_targeted_link_rel_filters ) {
+			wp_init_targeted_link_rel_filters();
+		}
+
 		$this->_changeset_data = null; // Reset so WP_Customize_Manager::changeset_data() will re-populate with updated contents.
 
 		remove_filter( 'wp_save_post_revision_post_has_changed', array( $this, '_filter_revision_post_has_changed' ) );
diff --git a/src/wp-includes/default-filters.php b/src/wp-includes/default-filters.php
index 66d64485d6..1319826212 100644
--- a/src/wp-includes/default-filters.php
+++ b/src/wp-includes/default-filters.php
@@ -128,19 +128,7 @@ foreach ( array( 'content_save_pre', 'excerpt_save_pre', 'comment_save_pre', 'pr
 }
 
 // Add proper rel values for links with target.
-foreach ( array(
-	'title_save_pre',
-	'content_save_pre',
-	'excerpt_save_pre',
-	'content_filtered_save_pre',
-	'pre_comment_content',
-	'pre_term_description',
-	'pre_link_description',
-	'pre_link_notes',
-	'pre_user_description',
-) as $filter ) {
-	add_filter( $filter, 'wp_targeted_link_rel' );
-};
+add_action( 'init', 'wp_init_targeted_link_rel_filters' );
 
 // Format strings for display.
 foreach ( array( 'comment_author', 'term_name', 'link_name', 'link_description', 'link_notes', 'bloginfo', 'wp_title', 'widget_title' ) as $filter ) {
diff --git a/src/wp-includes/formatting.php b/src/wp-includes/formatting.php
index dc4bf24648..4beb33cb8f 100644
--- a/src/wp-includes/formatting.php
+++ b/src/wp-includes/formatting.php
@@ -3095,6 +3095,52 @@ function wp_targeted_link_rel_callback( $matches ) {
 	return "<a $link_html>";
 }
 
+/**
+ * Adds all filters modifying the rel attribute of targeted links.
+ *
+ * @since 5.1.0
+ */
+function wp_init_targeted_link_rel_filters() {
+	$filters = array(
+		'title_save_pre',
+		'content_save_pre',
+		'excerpt_save_pre',
+		'content_filtered_save_pre',
+		'pre_comment_content',
+		'pre_term_description',
+		'pre_link_description',
+		'pre_link_notes',
+		'pre_user_description',
+	);
+
+	foreach ( $filters as $filter ) {
+		add_filter( $filter, 'wp_targeted_link_rel' );
+	};
+}
+
+/**
+ * Removes all filters modifying the rel attribute of targeted links.
+ *
+ * @since 5.1.0
+ */
+function wp_remove_targeted_link_rel_filters() {
+	$filters = array(
+		'title_save_pre',
+		'content_save_pre',
+		'excerpt_save_pre',
+		'content_filtered_save_pre',
+		'pre_comment_content',
+		'pre_term_description',
+		'pre_link_description',
+		'pre_link_notes',
+		'pre_user_description',
+	);
+
+	foreach ( $filters as $filter ) {
+		remove_filter( $filter, 'wp_targeted_link_rel' );
+	};
+}
+
 /**
  * Convert one smiley code to the icon graphic file equivalent.
  *
diff --git a/tests/phpunit/tests/formatting/WPTargetedLinkRel.php b/tests/phpunit/tests/formatting/WPTargetedLinkRel.php
index 5693f02973..08f8ac1021 100644
--- a/tests/phpunit/tests/formatting/WPTargetedLinkRel.php
+++ b/tests/phpunit/tests/formatting/WPTargetedLinkRel.php
@@ -83,4 +83,22 @@ class Tests_Targeted_Link_Rel extends WP_UnitTestCase {
 		$expected = '<p>Links: <a href="/" target="_blank">Do not change me</a></p>';
 		$this->assertEquals( $expected, wp_targeted_link_rel( $content ) );
 	}
+
+	/**
+	 * Ensure default content filters are added.
+	 *
+	 * @ticket 45292.
+	 */
+	public function test_wp_targeted_link_rel_filters_run() {
+		$content  = '<p>Links: <a href="/" target="_blank">No rel</a></p>';
+		$expected = '<p>Links: <a href="/" target="_blank" rel="noopener noreferrer">No rel</a></p>';
+
+		$post = $this->factory()->post->create_and_get(
+			array(
+				'post_content' => $content,
+			)
+		);
+
+		$this->assertEquals( $expected, $post->post_content );
+	}
 }