Legally, you don't have to give them anything. But Monzo are also not legally bound to give you a bank account, and can decide who to give accounts to based on the risk. And Know Your Customer / Anti Money Laundering (KYC/AML) regulations say they should ask for proof of ID.
Monzo turning the screw on this. Do you legally have to supply your salary, job details and tax residency info to a bank?