You can pay with bitcoin if you want. Bitcoin is not fully anonymous (but for that matter, neither is cash-in-the-mail since TLAs store photos of the outside of envelopes, but I digress). Kagi itself doesn't have the data needed to de-anonymize the transaction, so it's as anonymous as you can reasonably expect.
Bitcoin is not anonymous at all, a public ledger is the opposite of anonymous if anything. At best it's pseudonymous.
I think parent used Mullvad as an example as they actually support creation of accounts 100% anonymously, as you can literally mail them an envelope with cash.
