You are not obliged to register for VAT in the EU. Whether or not tax is due depends on the item purchased, the shipping destination, the buyer's location, the production (printing) location and the actual tax rate determined by the applicable state/country and/or local tax rates. More information can be found here.
When you try to place an order via the API Portal, you will see the calculated tax for that specific order.
Gelato does not provide tax, legal or accounting advice. This material has been prepared for informational purposes only, and is not intended to provide, and should not be relied on for, tax, legal or accounting advice. You should consult your own tax, legal and accounting advisors before engaging in any transaction.