Amazon – How to Share a Shopping Cart with Someone Else

As of now, no. However, the only way other people will see it is if they specifically search for you using your name or email address - If you want it to be private, just change your name to something else, and link only the friends you want to see it using share, and let them know the reasoning behind changing your name so they don't think you're insane. If you want it really, really private, change your email address associated with the account.

Hopefully Amazon will add a feature like you described in the future.

There doesn't appear to be a way to do this other than by scripting.

This seems like a good suggestion to put to Amazon though.