Although there are some blockchain solution that aimed at storing peoples data, as a sort of wannabe universal digital identity repository (i.e. https://www.ibm.com/blockchain/solutions/identity), they haven’t made a shine as far as I’m aware of. There’s probably terrain there for solutions similar to what digital certificates are, or combined, but that all seems to be below the line for now.

Having your data on a public ledger would need to be properly encrypted (otherwise, what would be the point), but the weak points are still going to be there: APIs and keys used to encrypt/decrypt the data. Any ideal solution should probably play along with trust as a key factor, and based on that, only share anonymized identity data to and fro.