Have you considered allowing them if you have a valid credit card on file. For example, I'm currently a Humble Monthly subscriber which already gives me a one click purchase options through the credit card on file.
Vultr, a VPS Host, accepts Bitcoins but started to require a valid credit card or Paypal purchase before accepting Bitcoins to prevent ToS violators who used Bitcoin.
It's not necessarily the case that someone would want to use Bitcoin for anonymity, it might just be a more convenient payment method or something else. Doesn't hurt to give people more places to spend their Bitcoin even if the circumstances are less than ideal.
In what way can Bitcoin be considered a meaningful alternative (however you define it) if you also have to input a valid credit card number (that, presumably, the merchant will run the traditional $1 verification charge on)?
The reality is that Bitcoin is less convenient than using a regular credit card (because, realistically, you're not going to be mining Bitcoin but rather you'll be buying Bitcoin using your regular credit card/bank account). I would argue that Bitcoin is also worse in every way (no chargebacks, wild fluctuations in the valuation of a unit of Bitcoin, etc.) if you also don't care about anonymity and the product you're buying is fully legal.
So it's like "providing an ID", and then paying. Even if bitcoin is not "anonymous" (pseudonymous), there's still the decentralised+cheap nature of it that's worthwhile.
Vultr, a VPS Host, accepts Bitcoins but started to require a valid credit card or Paypal purchase before accepting Bitcoins to prevent ToS violators who used Bitcoin.