arekperudenwpf

Meanwhile I’ve found a quick workaround.

I’ve added my special-purpose admin menu item which executes one line of code to change the option as I want.

Here is the procedure.

Using any file manager (in my case 000webhos ftp build-in tool) go to the folder of Theme used by your website (in my case public_html>wp-content>themes>twentyseventeen).
There is a file named functions.php.
Just in case of failure create a copy of original functions.php file (in my case the copy is named functions20210202.php).
Edit the file functions.php and at a very end of this file put short code.
This is the code in my case:

//AP20210202 adds admin menu item to perform requested operations
add_action( ‘admin_menu’, ‘register_my_menu_item_AP20210202’ );

function register_my_menu_item_AP20210202() {
    add_menu_page( 'AP20210202 special purpose admin menu item', 'AP20210202 execute programmed actions', 'manage_options', 'query-string-parameter', 'my_menu_item_AP20210202');
}

function my_menu_item_AP20210202
() {
    echo 'execution started!';
    update_option( 'require_name_email', '0' );
    echo 'execution finished!';
}

Save the functions.php file.
Go to wp admin menu page (https://YourSiteName.000webhostapp.com/wp-admin/).
Locate just created menu item (in my case named “AP20210202 execute programmed actions”).
Click on this menu item.
This executes part of the code: update_option( ‘require_name_email’, ‘0’ );
And you can verify in admin menu Settings>Discussion that the option “Comment author must fill out name and email” is now unchecked.

I’m not fully happy with this solution, because it’s against many rules, and, in case your Theme provider updates its functions.php file you need to enter the code again.
But it seems to be working.

Nevertheless I count of the community to find root cause why original admin menu doesn’t allow to switch off those options…

Thank you, RossMitchell,
nevertheless, I assume that this is not this problem because I can change other options (like numbers, texts, links, radio buttons, and even switch ON checkbox). The only thing which is not working is switching OFF checkbox (once switched on, they are not possible to switch off). ??