At the time of this writing (Q2 2021) Shopify supports a multi-currency checkout in specific regions for specific currencies when you use Shopify Pay (this was introduced in Q1 2019, read more details here: https://www.shopify.com/enterprise/multi-currency.

Due to an open issue in Shopify's API support for multi-currency, the app cannot support multi-currency in "Draft order mode". To support multi-currency, the app must be configured to use the "Discount code mode" checkout mode.

Read more about how to configure this here: https://support.discountninja.io/en/articles/6295059-checkout-mode