People need to do a bank run in every exchange (maybe even online wallets too) well before we reach the point of the hard fork, to ensure that they have control of their BTCs.
AlexGR raises an excellent point. If there is an upcoming contentious hardfork scheduled then the first things people are going to do is withdraw ALL their coins off the exchanges and out of any custodial services.
All those bitcoin alliance folks and corporates that have made their businesses out of holding on to other people's coins in custody should keep that mind whilst they are pushing for contentious hardforks.