Advanced custom fields sort repeater by date

I think this is not possible with the API functions provided by ACF. I would try to save the values to a temporary array first and then sort the values inside the array with php (using krsort() for example).

Something like this (just to give an idea):

while(has_sub_field('in_the_news')) {

    $date = get_sub_field('published_date');
    // $date = 19881123 (23/11/1988)

    // extract Y,M,D
    $y = substr($date, 0, 4);
    $m = substr($date, 4, 2);
    $d = substr($date, 6, 2);

    // create UNIX
    $time = strtotime("{$d}-{$m}-{$y}");

    $tmp_array[$time] = array(
        'link' => get_sub_field('link'),
        'title' => get_sub_field('title'),
        'publisher' => get_sub_field('publisher'),
        'date' => date('d/m/Y', $time)  
    );
}

krsort($tmp_array);

foreach($tmp_array as $entry ) {
    // your html ...
}

PS: It’s always better to save timestamps in a proper format (i.e. unix timestamp) in the first place if somehow possible. 19881123 is a strange date format.