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It already happens, it's called shotgun KYC. Go try to swap an OFAC sanctioned UTXO on Fixedfloat or another exchange.
Quantum or no quantum: 2 things will happen: 1) There will be 'soft' forks (likely many from time to time) in the future that 'freeze' coins; and 2) should any of those 'soft' forks ever get anywhere close to becoming relevent, conventional bitcoin will hard fork away from that freezing of coins. As such, the conventional bitcoin value prop will carry on regardless; but, there will also be corrupted chains that have been coopted for one special interest or another. Choose wisely.
In that case there is literally nothing we can do to prepare. If/when a CRQC appears Bitcoin will simply fail as it becomes easy to steal and no longer represents a hard asset.