I think you need to consider what the point of having the contacts in the CRM is if you do not include an email address.
Is you process to contact by physical address or phone number? What data field do you intend to use to ensure that the Customer is unique?
What will you do if you get two or more people named John Smith for example?
If you want to include your contacts as members of your site for some reason then you will need to use their email as the user id.
The Wix platform will let you do anything you want but it will involve additional work and probably coding if you don’t want to use the out of the box functionality.