Messages published onchain using Hive-Mail are quantum resistant, but this does not change anything in the way how Hive currently works. Hive like most blockchains is not expected to resist Shor's Algorithm when quantum computing reaches a certain number of logical qubits, likely ~2000. Meaning, at some point in the future, the algorithm used to derive key pairs in most blockchains including Hive will need to be changed. There's no reason for panic right now though.

Now, as I explained in my post, even after Hive changes algos to become quantum resistant, any encrypted messages published onchain prior to that will remain unchanged, i.e. easy prey to quantum computing, forever.