If miners would do a hard fork with different protocol rules, that would be called something other than bitcoin, maybe "segwit2x-bitcoin" or something.
If the exchanges trade 'segwit2x-coin' as Bitcoin, it will become 'Bitcoin', and the legacy coin, if it is possible to use at all, will have to be renamed.
It's not that simple. Exchanges and custodial wallets hold other people's funds, so they are not allowed to decide arbitrarily which chain is "Bitcoin". That would be regulatory suicide.
