There are more significant problems with the UK's democratic process than whether or not the result of a non-binding referendum - that should never have taken place in the form that it did; that featured campaigns dominated by lies, populist dog-whistling & foreign intervention; where the winning side received a minority of the total electoral votes possibly cast - is respected.
This is a red herring.
A hard Brexit suits burner politically for the same reasons it suits Corbyn.
This is the state of our country at the moment.
Please, do not humour or give credence to those on the hard right or hard left.
They, and their extreme views, can fuck off. Do not let them drag the centre to the right or the left.
The UK needs to grow the fuck up, dispense with political tribalism, reform its press, and embrace mature consensual politics. Where dialogue and compromise trump childish squabbling and cult of personality.
Then and only then, will I listen to arguments about the democratic legitimacy of referenda that, as you say, have been abused by populists over the course of history.
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Sure. I agree. The problem in this case is that the democratic legitimacy of the referendum itself has always been questionable.
For me, it's quite straight forward: I disagree completely & utterly with anyone who says that the referendum result is a mandate for a Hard Brexit, and it's something I'm prepared to fight against. An incremental Brexit / May's Brexit? I would have gone along with. But a hard Brexit? Nah.