CheeseMmmm what are you on about?
An Irish person has the right to live in the UK, to vote in the UK, and to travel between the UK and Ireland. There are numerous agreements in place. There is no need for a British passport.
Removing a British passport from someone who previously had both an Irish and a British one would not prevent that person from travelling to, living in, working in, voting in, the UK.
You can't exile someone from NI to ROI because that person can just walk across the border again quite legally. They could get on a boat or a plane to the UK mainland.
Removing a British passport would be largely symbolic.
The government has been able to do this since just after the 7/7/2005 bombings. The main change in this bill is about being able to do it to people who are incommunicado, like off fighting for ISIS somewhere in the Middle East. The Home Office said: “British citizenship is a privilege, not a right. Deprivation of citizenship on conducive grounds is rightly reserved for those who pose a threat to the UK or whose conduct involves very high harm. The nationality and borders bill will amend the law so citizenship can be deprived where it is not practicable to give notice, for example if there is no way of communicating with the person.”
There are some online quotes from handwringers who think this makes their own citizenship second rate, as Lobster alluded to. But dual nationality is in itself a privilege - I have the ability to claim a second passport and choose not to, for example. But am I in danger of being deported? No, because I'm not a spy or a terrorist. In fact, it's quite easy not to be a spy or a terrorist. The vast majority of us "foreign types" manage it quite easily. 