I see you have removed the tax from product “Beanie”, try enabling the tax but with Zero rate, that’s my situation. You can see in my screnshots there is existing VAT but it is free (0,00 kn in my currency).
I am using default Woocommerce tax settings, the only thing I did is through code I made Zero rate to a specific user role.
if ( is_user_logged_in() && in_array( 'fizicka', $user->roles ) ) {
$tax_class = 'Zero Rate';
}