Thus, upgrading the protocol/code to change the encryption to something quantum-resistant should be no more controversial a change than segwit. The community has already answered the "is it still Bitcoin". Yes it is, protocol and code is free to change given longest-chain consensus.
The problem will be what to do with legacy addresses. Never before have issued coins been forcibly deleted by a BIP. It could turn out that legacy addresses (including Satoshi's) that fail to have their coins moved after a deadline must be considered compromised and burned/destroyed. That has no precedent with bitcoin, although it does with ETH.
Anyone know if there's a way out that doesn't require this? Obviously there's no way to ensure all legacy address coins are moved by the deadline.