I don't think Andy Burnham, or for that matter anyone in the Labour party, or anyone outside whatever iteration of Farage's party and the Tories (and of those, not all of them) treated it like a "divine mandate" or with reverence.

Look, here we're all annoyed about Brexit, because it's shit and we knew it would be. We'd like it to be reversed as soon as possible. But undoing the most significant change to the UK's constitution a mere 6 years after it was enacted and 10 years after it was decided is unthinkable. So we're not being cautious now because of "reverence" for Brexiter's preferences, but because it is a think that deserves to be treated with caution. It was a decision that was taken with rank recklessness, but unfortunately that doesn't mean we can undo it with the same recklessness. That won't solve the problems; it will help cement the idea that membership of the EU, or other serious, difficult, significant changes to the country can be done and undone on a whim.