BTC rich people are on both sides of the debate, expect to see some dumping all around as they make their positions known.
If one chain has 10% hashing power, for less or equal to 14 days the transactions could take 10 times more to validate. But that's assuming markets aren't correcting miners in the "right" direction in the meantime. Who wants to waste electricity on undervalued coins?
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Considering most of BTCs have been mined at the time bitcoin core had no competition; I'd say BTC rich people would tend to side with them. Because of emotional attachment, economic ties, and most importantly the dumb but very real reason of software maintenance.
I don't know if non-miners also check the difficulty or difficulty calculations, but if they do, even the minority chain can't fork without affecting existing users.
In that case everyone would need to fork in which case you're back to square one: what to do with the users that can't or don't want to fork. And if you need to fork anyway, it makes little sense to go with the minority chain.
In the end, miners mine what people buy. It's that simple.
Any speculation as to what happens if all miners move as one, motivated by ideology instead of economics, is just that.
I'm pretty sure the backlash against both the hostile miner and all of Bitcoin combined would not be worth it, except in a Joker 'Let's burn all this cash' kind of way.
The worst a majority can do, is to create a new longest chain without any transactions. But in that case the transactions would still exist and can be mined again later (and supplanted again later).
But that would require a miner to want to spend resources to hurt the minority fork.
If the minority fork is big enough to be a threat, that would require a lot of 'majority' miners to work together to pull off this attack, which would lead to a tragedy of the commons situation. Any majority miner who doesn't participate in the attack would gain.
If the minority fork is small enough to be a toy for a single miner, it still doesn't make sense to put in the still substantial effort.
Just look at the Ethereum fork. Afaik there have been no shenanigans pulled of by a majority miner on the minority fork, even though it's only about 10% of the size.
It's going to be 2 legitimate currencies that are going to differ in value in exchanges. And each current BTC holder will be able to spend 2 coins (provided they take precautions against replayability; like making at first a double-spend to different wallets on the two chains separately)
Now the question is: what will the most BTC-rich people do?