Just following up for anyone that might come across a similar issue in future…
Version 1.3.5 of the Shippit module resolves this issue, so that taxation amounts on the shipping quote is based on your WooCommerce taxation preferences.
If you still encounter a similar error such as “The TaxType code ‘EXEMPTEXPENSES’ cannot be used with account code ‘{{ACCOUNTID}}’”, you may need to confirm that the WooCommerce account ID and Xero Shipping Account Type matches – this is, whether shipping costs are treated as Expenses or as Income.
Having the incorrect account setting in the Xero integration will cause the Xero integration to fail, as it’s setting a tax type not supported by the account.