We don't require this for you to open a website, but almost all governments will require you to have this. The penalty is usually quite severe, so it is a requirement eventually. In most cases registration is free, or only required after a minimum of sales.
So it depends where you are, but you can sign up with Shopify and we will ask for the correct information along the way.
In the US you require an EIN with the Shopify Payments gateway and you can sign up for both the gateway and the EIN freely.
You can also accept payments with other gateways on Shopify, and they will then require the information from you, but that would be along their terms.