Proving you're a real person doesn't need to be at odds with the user's privacy concerns.
Look at the verification system used by risky subreddits for example, you only have to provide a few pictures of yourself posing with a sign with your username written on it from different angles. Currently hard to replicate by bots or photoshop, and privacy preserving.
Short of reaching AGI there will always be tasks that can differentiate humans from machine and won't require the users to post a photo of their passport or phone number.
Well in that system you don't have to show your face, your identity is not compromised. And you're already planning on showing your body so no additional information is asked by the human-proving system that'd help identify you.
But that's just an example, you can think of a 100 even more private implementations that give proof of humanity without giving proof of identity.
Look at the verification system used by risky subreddits for example, you only have to provide a few pictures of yourself posing with a sign with your username written on it from different angles. Currently hard to replicate by bots or photoshop, and privacy preserving.
Short of reaching AGI there will always be tasks that can differentiate humans from machine and won't require the users to post a photo of their passport or phone number.