I found out you could identify ajax requests by the following if-statement
if (defined('DOING_AJAX') && DOING_AJAX)
So problem solved using
add_action('init', 'set_global_pixelcapival');
function set_global_pixelcapival() {
if (defined('DOING_AJAX') && DOING_AJAX) {
} else {
global $pixelcapival;
$pixelcapival = pixelcapival();
global $prev_pixelcapival;
$prev_pixelcapival="";
if(isset($_COOKIE['pixelcapival'])) {
$prev_pixelcapival = $_COOKIE['pixelcapival'];
}
setcookie('pixelcapival', $pixelcapival, time() + 1200, "https://wordpress.stackexchange.com/");
}
}