Not on the same chain.  Each chain becomes it's own coin.  Coins from before the fork are effectively split into 2 identical coins (1 on each chain).  Coins spent on one chain can't be double spent on that chain, but if you don't manage your transactions carefully enough you can be forced to send the twin coins on the other chain to the same address on that chain.

Those that are technically aware enough can take precautions to prevent this, but the average user is likely to have a problem and not know it until it is too late.


A contentious fork is already likely to be pretty damaging.  Replay attacks are a known vulnerability with known methods of avoiding the problem.  They aren't likely to make it much worse.


I think both SW and BU are not great ideas.  They are each attempting to be "good enough", but they each have issues. I'm not sure if there is a good solution.  Perhaps we're about to discover that the whole cryptocurrency experiment is unsustainable.