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Why change the hash function?
It's not SHA256 that is the problem, but ECDSA.
signatures are more urgent but hash functions are not threat proof either.
All hash functions based on universal-hashing have been shown to be threatened by Bonnetain 2021. It's not impossible the same will happen with Merkle Damgard constructions like SHA will have simmilar algorithms.
But worry not, there are many post-quantum secure hash functions in academia being discussed. They will be ready soon - many many years before quantum computers will have bit lengths long enough
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right, it's a risk because it's believed to be true that it is possible this will happen.
This belief is the main ingredient of the fud. Quantum resistant algorithms are well known to devs, so it would be a nothingburger as the protocol would make the adjustment rather quickly
we'll computer our way into the eternal realm...
If it indeed turns out to be an existential threat, a hard fork involving hashing algorithm change would be the most effective solution and you can safely bet that most plebs will be on board i.e. it won't be contentious in any way. This has been brought up on different occasions over the past five years at least and this is the proposed solution. Not sure miners would eagerly support it as current mining equipment would be made obsolete as a result, but it's better than having your earnings drop to zero