So to sum it up, for those who may not want to read the article (don't worry though, it's not super long)--you can't do a traditional registry at Anthropologie. However, what you can do is make a 'wish list' and you can make it public. There are a couple issues--you can't buy from a wish list in-store--it has to be done online. Not everybody does things online and then you have to pay for shipping and handling. Also, when something is ordered off the wish list--the wish list creator gets an email from Anthropologie saying 'This was bought off your wish list' so that you know to remove it to avoid duplicates--but then there is the risk of the people that do want to avoid the shipping and handling and might have one in a short driving distance--well those purchases won't be told to the wish list creator and so then duplicates are a possibility.
Personally, I would risk the duplicates. I love Anthropologie, too. But I know my "audience" (the guests), and most of them are the types that would/do include gift receipts just in case, plus many are Internet-savvy, so my risk of duplicates would be low.
If your guests are likely to be that way, or if you're OK with giving away duplicates, I think it's worth the risk.
But I'd check with Anthropologie to see what their policy is on gifts you receive with no receipt. They might let you exchange for store credit. Bummer, right?
I'd also, if you want to go to the trouble, contact them to ask about doing a traditional registry since their "wish list" deal is an awkward arrangement. Their policy might not get changed in time for you to benefit, but maybe it will help future brides?