Form validation evaluation to avoid exploits

Please advise if the form validation script below is secure enough to avoid most types (all types?) of contact form exploits? I ahve found this script online, added some extra php finctions in hope to make it safer, but not complitely sure if it is good for the purpose.

if ($_SERVER["REQUEST_METHOD"] == "POST" && !empty($_SERVER['HTTP_X_REQUESTED_WITH']) && strtolower($_SERVER['HTTP_X_REQUESTED_WITH']) == 'xmlhttprequest') {
    // Get the form fields and remove whitespace.
    $name = strip_tags(trim($_POST["name"]));
    $name = str_replace(array("\r","\n"),array(" "," "),$name);
    $email = filter_var(trim($_POST["email"]), FILTER_SANITIZE_EMAIL);
    $message = strip_tags(trim($_POST["message"]));

    // Check that data was sent to the mailer.
    if ( empty($name) OR empty($message) OR !filter_var($email, FILTER_VALIDATE_EMAIL)) {
        // Set a 400 (bad request) response code and exit.
        //http_response_code(400);
        echo "Oops! There was a problem with your submission. Please complete the form and try again.";
        exit;
    }

    // Set the recipient email address.
    // FIXME: Update this to your desired email address.
    $recipient = "email_here";

    // Set the email subject.
    $subject = "New contact from $name";

    // Build the email content.
    $email_content = "Name: $name\n";
    $email_content .= "Email: $email\n\n";
    $email_content .= "Message:\n$message\n";

    // Build the email headers.

    $email_headers = "MIME-Version: 1.0\r\n";
    $email_headers .= "Content-type: text/html; charset=utf-8\r\n"; 
    $email_headers .= "From: $name <$email>\r\n";
    $email_headers .= "Reply-To: $email\r\n";
    $email_headers .= "Return-Path: $email\r\n";
    $email_headers .= "Organization: Bilingual Counselling\r\n"; 

    // Send the email.
    if (mail($recipient, $subject, $email_content, $email_headers)) {
        // Set a 200 (okay) response code.
        //http_response_code(200);
        echo "Thank You! Your message has been sent.";
    } else {
        // Set a 500 (internal server error) response code.
        //http_response_code(500);
        echo "Oops! Something went wrong and we couldn't send your message.";
    }

}