In the US you cannot run that company: if you accept money in exchange for goods (or even sometimes services), and are not a registered non-profit, you need to pay sales taxes on the sales, must declare any residual as income, and the people giving you the money cannot claim it as a write off.
Regretsy is in the EU, not the US, but I don't believe that changes the point. In the EU, everything that is traded, whether it be a good or a service, is subject to a "value added tax". (Note: this applies to you even if you are not yourself living in the EU; if you sell products to EU customers online, you must collect and remit VAT if you are above their threshold.)
These taxes can be quite high: up to 25% of the receipt. You are only responsible for the "value added" (so you subtract your costs), but the way you subtract your costs is very similar to expense structure in the US: the cost you declare has to be to another VAT-registered organization, and you need to keep whatever receipts and documentation is required to defend the costs later.
I am simply having a very difficult time seeing how this specific setup was, in the eyes of the law, any different from Ikea selling chairs: they were selling products, and selling products is a highly regulated business with a large number of taxes that have to be considered. You cannot just throw up a website and willy-nilly throw money around.