When taxes are country specific they don’t show in the cart totals

This is a matter of configuration:

This way taxes will be shown on the cart page:

But because the address can be changed at checkout, this isn’t and can’t be conclusive – like it’s stated taxes are estimated and will be updated on checkout.

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Update:

Last week I quickly looked at the woocommerce code, but didn’t have time to complete my answer. What I found is that there is a filter – woocommerce_matched_rates – you can hook into. The filter is part of the get_rates() function inside class-wc-tax.php. Below some code sample to begin with:

add_filter( 'woocommerce_matched_rates', 
            'wpse115734_wc_customer_based_tax_on_cart' );

function wpse115734_wc_customer_based_tax_on_cart( $matched_tax_rates="", $tax_class="" ) {
    global $woocommerce,$product;
    $tax_class = sanitize_title( $tax_class );
    $_taxobj = new WC_Tax();

    list( $country, $state, $postcode, $city ) = $woocommerce->customer->get_taxable_address();
    $shop_country = $woocommerce->countries->get_base_country();

    if ( ! ( $country == $shop_country ) ) {
        $matched_tax_rates = $_taxobj->find_rates( array(
            'country'   => $country,
            'state'     => $state,
            'postcode'  => $postcode,
            'city'      => $city,
            'tax_class' => $tax_class
        ) );
        return $matched_tax_rates;
    } else {
        $matched_tax_rates = $_taxobj->get_shop_base_rate( $tax_class );
        return $matched_tax_rates;
    }
}

As you can see this hooks into the filter and does some conditional check based on the shop base and the customer country. This is working for me, the taxes is shown based on the customer address, if it differs from the shop country. But like I said this is to begin with, because I did no further testing, it’s merely proof of the possibility.