Stuck In a Redirect Loop

You also need to check if the user is on that particular page or not. If he is on that page, then there is no need to redirect him/her again.

Change your else to this:

if(is_user_logged_in() && function_exists('pmpro_hasMembershipLevel') && pmpro_hasMembershipLevel()) {
    global $current_user;
    $current_user->membership_level = pmpro_getMembershipLevelForUser($current_user->ID);
    echo 'Membership Level: ' . $current_user->membership_level->name;
} else {
    if( ! is_page('page-slug') ){
        wp_redirect('/my-account/orders/');
        exit;
    }
}

In which page-slug is the slug of the page you are redirecting your users to.