Why do taxes apply on Free Gift items?
Starting from version 2.11.0, the Free Gift for Magento 2 extension provides the option to define whether a free gift comes as a $0 product or as a product with a 100% discount. The setting is available in Amasty → Free Gift → Configuration → Messages And Notifications Settings.
The point is that if the Free Gift promo item is set to be displayed as product with the 100% discount, Magento considers such promotion as a usual cart price rule giving the 100% discount. Therefore, such promotions should comply with the Magento tax configuration.
If you don't need any taxes to apply on Free Gift items, the following tax setup is recommended in Stores → Configuration → Sales → Tax → Calculation Settings:
Let's check the result using a cart price rule which provides the gift once the cart subtotal exceeds $50 (the rule can be created at Marketing → Cart Price Rules):
As a result, the free gift item is provided with the 100% discount including tax: