The store requires that the person be a user (i.e. have an email/password) on the site, because some of the functionality requires knowing who the user is, and who the user’s family members are.
The store is not exposed to the public.
The one alternative is that if you include store products in the Sunday newsletter (this is an option on the product), a recipient of the newsletter can click on store items in the newsletter and add them to their cart without having to login first. They can then add additional items to the cart. But they must have directly received the newsletter for this to work.