How to change users avatar with specific e-mail addresses

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Two things:

  1. The $id_or_email can be an integer (a user ID), a string (Gravatar MD5 hash or user email) or an object (e.g. a WP_User instance), so you can’t simply do $mail = $id_or_email->comment_author_email;.

  2. The email addresses in your list are all in the form of anonimus_<number>@anonimus.com, so instead of defining that long array, you can simply use regular expression (RegEx).

(Update) Plus another thing:

  1. Instead of the get_avatar filter/hook, you should probably just use the pre_get_avatar_data hook since in your my_get_avatar() function, you’re simply changing the avatar URL.

    That way (i.e. using the above hook), your callback would also work with get_avatar_url() and not just get_avatar().

So just remove the add_filter('get_avatar', 'my_get_avatar', 10, 5); from your code (and remove also the my_get_avatar() function), and then use the following instead:

add_filter( 'pre_get_avatar_data', 'my_pre_get_avatar_data', 10, 2 );
function my_pre_get_avatar_data( $args, $id_or_email ) {
    // First, get the user's ID or email for unregistered comment authors.
    if ( is_numeric( $id_or_email ) ) {
        $user = get_user_by( 'id', $id_or_email );
    } elseif ( $id_or_email instanceof WP_Comment ) {
        $email = $id_or_email->comment_author_email;
        $user = get_user_by( 'id', $id_or_email->user_id );
    } elseif ( $id_or_email instanceof WP_Post ) {
        $user = get_user_by( 'id', $id_or_email->post_author );
    } elseif ( $id_or_email instanceof WP_User ) {
        $user = get_user_by( 'id', $id_or_email->ID );
    } else {
        $user = get_user_by( 'email', $id_or_email );
    }

    // For registered users, get the email in the database.
    if ( empty( $email ) && $user && ! is_wp_error( $user ) ) {
        $email = $user->user_email;
    }

    // Then check the user's email and use the custom avatar, if applicable.
    if ( ! empty( $email ) && preg_match( '/^anonimus_\d+@anonimus\.com$/', $email ) ) {
        $args['url'] = 'http://example.com/wp-content/anonimus-avatar.png';
    }

    return $args;
}

But if you’d rather use the get_avatar hook, then please let me know or just check this answer’s revisions.

In response to your comment:

please help to apply this to AMP pages too. filter
ampforwp_get_comments_gravatar

You should really ask in the plugin support forums, but let’s make an exception just this time, and you can try the following, which overrides the ampforwp_get_comments_gravatar() function — yes, there’s a hook with the same name, but I don’t think it will work (because their code doesn’t pass the $comment variable to the hook callbacks).

if ( ! function_exists( 'ampforwp_get_comments_gravatar' ) ) :
    function ampforwp_get_comments_gravatar( $comment ) {
        global $redux_builder_amp;

        if ( ! empty( $redux_builder_amp['ampforwp-display-avatar'] ) ) {
            return get_avatar( $comment );
        }

        return '';
    }
endif;

That is untested, but it should work. And if you need further customization help, please, ask/post another question.