Short Circuit a post save in WordPress and give the user a notice saying why.

short-circuit.php

<?php

namespace JPB;

function wp_insert_post_data( $data, $postarr ){
    if($data['foo'] !== 'bar' || $data['baz'] !== 'bat'){
        wp_redirect( add_query_arg( array( 'post' => $data['ID'], 'action' => 'edit', 'message' => 11 ), admin_url( 'post.php' ) ) );
        exit;
    }
    return $data;
}

add_filter( 'wp_insert_post_data', '\\JPB\\wp_insert_post_data', 10, 2 );

function messages( $messages ){
    $messages[11] = 'You did not fill my two fields out!';
    return $messages;
}

add_filter( 'post_updated_messages', '\\JPB\\messages' );