When tax exempt for EU Tax registered subjects is active, by default Prestashop core does not set (tax excl.) properly for guests. To solve it, update classes/Product.php, method initPricesComputation.

Edit file: classes/Product.php and modify else { ... } clause, as highlighted:

public static function initPricesComputation($id_customer = null)
{
    if ((int)$id_customer > 0) {
        $customer = new Customer((int)$id_customer);
        if (!Validate::isLoadedObject($customer)) {
            die(Tools::displayError());
        }
        self::$_taxCalculationMethod = Group::getPriceDisplayMethod((int)$customer->id_default_group);
        $cur_cart                    = Context::getContext()->cart;
        $id_address                  = 0;
        if (Validate::isLoadedObject($cur_cart)) {
            $id_address = (int)$cur_cart->{Configuration::get('PS_TAX_ADDRESS_TYPE')};
        }
        $address_infos = Address::getCountryAndState($id_address);

        if (self::$_taxCalculationMethod != PS_TAX_EXC
            && !empty($address_infos['vat_number'])
            && $address_infos['id_country'] != Configuration::get('VATNUMBER_COUNTRY')
            && Configuration::get('VATNUMBER_MANAGEMENT')) {
            self::$_taxCalculationMethod = PS_TAX_EXC;
        }
    } else {

        self::$_taxCalculationMethod = Group::getPriceDisplayMethod((int)$customer->id_default_group);
        $cur_cart                    = Context::getContext()->cart;
        $id_address                  = 0;
        if (Validate::isLoadedObject($cur_cart)) {
            $id_address = (int)$cur_cart->{Configuration::get('PS_TAX_ADDRESS_TYPE')};
        }
        $address_infos = Address::getCountryAndState($id_address);


        if (self::$_taxCalculationMethod != PS_TAX_EXC
            && !empty($address_infos['vat_number'])
            && $address_infos['id_country'] != Configuration::get('VATNUMBER_COUNTRY')
            && Configuration::get('VATNUMBER_MANAGEMENT')) {
            self::$_taxCalculationMethod = PS_TAX_EXC;
        } else {
            self::$_taxCalculationMethod = Group::getPriceDisplayMethod(Group::getCurrent()->id);
        }
    }
}