Wordpress - Apply remove_filter only on one page

I know this is an old question, but I thought I'd chime in for anyone looking to do this in a more general sense (e.g. not in conjunction with plugin output) and say that you could also just add this to your functions.php file:

add_filter('the_content', 'specific_no_wpautop', 9);
function specific_no_wpautop($content) {
    if (is_page('YOUR PAGE')) { // or whatever other condition you like
        remove_filter( 'the_content', 'wpautop' );
        return $content;
    } else {
        return $content;
    }
}

I suggest creating a page template for the "one page includes a php file (with exec-php)". Then add an if statement around the remove_filter(...) statement.

if (!is_page_template('my-page.php'))
  remove_filter('the_content', 'wpautop');

Hope it works. ;P

Like mroncetwice, I too realize that this is an old question; however, I came to this thread looking for an answer when I saw his. I decided to improve upon it (in terms of suiting my own situation) and am sharing the results with the hope that it may also help others.

---

Turn wpautop on or off by default and list any exceptions:

/**
 * Allow or remove wpautop based on criteria
 */
function conditional_wpautop($content) {
    // true  = wpautop is  ON  unless any exceptions are met
    // false = wpautop is  OFF unless any exceptions are met
    $wpautop_on_by_default = true;

    // List exceptions here (each exception should either return true or false)
    $exceptions = array(
        is_page_template('page-example-template.php'),
        is_page('example-page'),
    );

    // Checks to see if any exceptions are met // Returns true or false
    $exception_is_met = in_array(true, $exceptions);

    // Returns the content
    if ($wpautop_on_by_default==$exception_is_met) {
        remove_filter('the_content','wpautop');
        return $content;
    } else {
        return $content;
    }
}
add_filter('the_content', 'conditional_wpautop', 9);