If I am understanding this correctly, if users want to purchase an item they need to register again? I have used Zen Cart standalone before for other sites, but the purpose I am moving over to Xoops is not to have multiple log-ins for the same site.
If this is the case with Zen Cart on Xoops can anyone point me to a different Shopping cart that I can integrate in my site with out requiring a second log in.

There isn't one

At this time there is not a working shopping cart for Xoops. Wishcraft is working on one but currently a working one does not exist.

The problem is, you need much more info about users to set up an account for ecommerce than a CMS would ever require. Combining the two under one registration seems like a good idea, but asking for real names and full address details would dissuade many people from registering on your site if they don't particularly want to use the shop feature.

I would redirect users to a standalone ecommerce app that is right up to date and has a track record of reliability with order processing and payment gateways.

Ecommerce software need to be bullet proof and as site operator, you can bring a lot of trouble down on your head if you use a buggy app that messes up transactions.

I agree that people will find it fishy if you ask them their personal data during regular procedure of regustration. So double registration looks like a good way out