I think we should first ask ourselves how legal is that? I'm curious how the bank can ever demand that, it is just not their business by any metric. It is like your employer telling you that you should not spend your money on things that he doesn't quite like. You may love apples and he may love oranges. Did anyone sue the bank yet? Or is this real?
When it comes to banking lots of employees will sign contracts agreeing that they can't have personal trading accounts on regular markets. There's no reason why they'd allow them on irregular ones either.
There may be a division between retail banking and investment banking employees but restrictions are there.