KYC faced the real security issues. Someone can steal your data by hacking the platform and use it for criminal purpose. But in other hand, crypto world still finding the best ways how to protect crypto transaction form money laundery, human trafficking and drugs transaction.
I think, its a big responsibelity to keep KYC data safe. If not, crypto will had bad ending.
Its as safe as providing your Kyc details to any private sector Banks. Digital Wallets are now regulated by the RBI. At the end its the consumer trust what matters. Until a data breach happens all public and private sector banks and companies are good so having faith , trust and confidence is all what you can do.