I think the fact that Brexit is rarely talked about socially is actually a symbol of the division. I think about it a lot but only talk with those members of my friends and family that I know voted the same as me as I don't want to start an argument.
The main trouble is that no sort of compromise was sought and we seem to be left with only the most polarising versions. Whatever happens, there is going to be some very angry people. If we were to cancel it, a lot of people who voted leave would be angry. If we exit with no deal, people who want to remain (and people who wanted to leave with a "soft" option) will be angry. If we had gone with some sort of Norway-style arrangement,bit would have fulfilled the mandate of the referendum (which was simply to leave the EU) but been palatable to most people who voted remain. Unfortunately the TM government immediately ruled out such a compromise.
Personally I think the only way that something of this magnitude could ever be done is gradually. Leave, but with a very close relationship. Give it a few years and see how things re going. Leave the door open to either gradually disentangle further if things are going well or leave the door open to rejoin if things are going badly and judging the mood of the public (which will start to include new generations of voters).
That option is still very much on the table, and is pretty much what Angela Merkel meant when she referred to 30 days as it could pretty much be sorted in that length of time. It was the most obvious solution straight after the vote. Unfortunately, government rhetoric, whipped up by the media, have left that option almost impossible now.