diff -u b/core/modules/user/config/schema/user.schema.yml b/core/modules/user/config/schema/user.schema.yml
--- b/core/modules/user/config/schema/user.schema.yml
+++ b/core/modules/user/config/schema/user.schema.yml
@@ -10,6 +10,9 @@
     verify_mail:
       type: boolean
       label: 'Require email verification when a visitor creates an account'
+    register_password_set:
+      type: boolean
+      label: 'Require people to choose a password during registration.'
     notify:
       type: mapping
       label: 'Notify user'
diff -u b/core/modules/user/tests/src/Functional/UserRegistrationTest.php b/core/modules/user/tests/src/Functional/UserRegistrationTest.php
--- b/core/modules/user/tests/src/Functional/UserRegistrationTest.php
+++ b/core/modules/user/tests/src/Functional/UserRegistrationTest.php
@@ -201,7 +201,7 @@
     $this->drupalGet('user/login');
     $this->assertSession()->statusCodeEquals(200);
     $this->submitForm($edit2, 'Log in');
-    $this->assertSession()->responseContains('The username ' . $name . ' has not been activated or is blocked.');
+    $this->assertSession()->pageTextContains('The username ' . $name . ' has not been activated or is blocked.');
 
     // Try to activate the user.
     $new_user->activate();
@@ -383,13 +383,13 @@
     $this->drupalGet('user/register');
     $this->assertSession()->statusCodeEquals(200);
     $this->submitForm($edit, 'Create new account');
-    $this->assertSession()->responseContains("The username {$account->getAccountName()} is already taken.");
+    $this->assertSession()->pageTextContains("The username {$account->getAccountName()} is already taken.");
 
     $edit = ['mail' => $account->getEmail(), 'name' => $this->randomString()];
     $this->drupalGet('user/register');
     $this->assertSession()->statusCodeEquals(200);
     $this->submitForm($edit, 'Create new account');
-    $this->assertSession()->responseContains("The email address {$account->getEmail()} is already taken.");
+    $this->assertSession()->pageTextContains("The email address {$account->getEmail()} is already taken.");
   }
 
   /**
@@ -451,7 +451,7 @@
     $edit['test_user_field[0][value]'] = '-1';
     $this->submitForm($edit, 'Create new account');
     $this->assertRegistrationFormCacheTagsWithUserFields();
-    $this->assertSession()->responseContains("{$field->label()} does not accept the value -1.");
+    $this->assertSession()->pageTextContains("{$field->label()} does not accept the value -1.");
 
     // Submit with valid data.
     $value = rand(1, 255);