In the last week, a lot of exchanges including coinbase and other exchanges such as Bitfinex and Kraken clearly stated that they are going to treat Bitcoin Unlimited as an alternative coin while the current one stays BTC.
Honestly, It's better to have your coins somewhere where you actually control your private keys and not rush into doing anything until things are clear for the community, playing around and trying to switch while you don't have an idea on the process could lead to bad consequences.
Actually, Coinbase didn't sign the statement and seemed to think that it was too pro-Core so their position is a bit less clear.
I suppose if it's treated as an alt on most exchanges though, maybe if you were holding Bitcoin on exchanges they would just still be represented as BTC and they would probably rob you of the BTU that they would receive.
Online wallets aren't quite like exchanges though because they recognise that you're trying to hold Bitcoin, which could be expressed as BTC or BTU or both, whereas exchanges will view it more like you chose to hold BTC so that's what you will keep.
I hope that some reputable services like Blockchain will allow the users both of their coins.
