In fact, I don't actually use it, but as an experiment I once set up and fooled around with an OpenRouter account over Tor. It did demand an email address, and I gave it a Proton account also set up over Tor. Both were paid for with anonymous cryptocurrency: Monero gatewayed via some random exchanger.
Whereas I never signed up for an Anthropic account because the first screen I hit demanded a phone number. I mean that was the only thing on the screen, and you weren't going anywhere until you provided it. It's been quite a while, though.
Perhaps there are different paths to getting accounts.