You can buy prepaid debit cards in cash and load them with up to $500 at almost any Walmart (and probably a lot of other locations). I like the OneVanilla prepaid debit cards because I can use them online (but only with US-based vendors -- no international transactions) and put anything I want (such as "Hacker News") as the cardholder name.

Another great alternative is privacy.com which allows you to create anonymous credit cards (your bank is then debited). While the vendors won't know who you are privacy.com certainly does and they use Plaid on the back end so they likely know as well. VISA just tried to buy Plaid; someone eventually will acquire them (maybe Google?) so keeping your financial info private via privacy.com might not be something that works long-term.