According to Bitfinex' announcement, they say there will be continuous trading:

"We have a responsibility to foster, maintain, and support orderly markets that trade continuously 24/7/365. With a hard fork that lacks clear community consensus, we cannot suspend operations and wait for a winner to emerge. Leveraged trading requires that our markets operate continuously. On operational requirements alone, we must designate such forks as new assets."

but NOT CONTINUOUS DEPOSITS/WITHDRAWALS:

"At the moment of the fork, all deposits and withdrawals for both BTC and B2X will be halted until we are able to: 1. ‘taint’ our customers’ bitcoins to ensure withdrawals cannot be replayed on both chains; and, 2. ensure that we can properly credit deposits in the event a transaction is replayed on both chains. We expect this process to require at least 24 hours, and potentially significantly longer. If the the event happens, announcements will be made throughout the process to keep everyone up to date."