Thank you for reaching out to the Community! You can certainly allow for customers to check out in their local currency if using Shopify Payments. To achieve this, you will want to ensure you have set up Shopify Markets under Settings > Markets, where customers will then be able to browse, check out, and receive refunds in their local currency. We have a list of the following currencies that supported with the use of Shopify Markets.
It's important to note that a country selector will still be required to allow customers to select their local country or region to begin shopping in their respective currency.
If you are not using Shopify Payments, customers will be able to browse and shop in their preferred currency though Multiple Currencies, but will check out in the shops default currency.
Please let me know if you have any other questions!