Besides Bitcoin can always fork to become a quantum computer resistant before that threat happen.
That's the easy part. The difficult part is dealing with the millions of bitcoins that will reenter circulation from bitcoins sitting in vulnerable addresses.
We had experience fork before, so I think both developers and holders have experience in this kind of situation so no matter how hard or risky it is, I believe it will be done successfully. Aside from that, several users had a first hand experience on updating/swapping their cryptocurrency holdings since this thing often happen in altcoins. They might be different cryptocurrency or value involved, but I think the drill is almost the same.
FUD.
You don't think the devs of a $150b asset would let it go to "0" do you? If anything like that starts to possess a threat to Bitcoin, there will be either a HF, or a quick fix but it will be fixed.
That is why I think people are just over reacting about this issue but I do understand them. There is nothing we can do but trust our Bitcoin developers to maintain the Bitcoin security intact and QC proof/resistant.