I simply don't buy that line that liberals have done something oh so terrible to the brexiteers that absolves the brexiteers from blame for their own action.
Also it is truly bizarre to blame "liberals" (in the sense of the word that I think that you are using it, i.e the way it is predominantly used in the US) for neoliberalism. Neoliberalism is a conservative fetish. Yes they got a lot of help from the center-left, but lets not forget who's child it is.
The majority of people who voted Brexit on July are not ''brexiteers'', so with that noted we have to ask ourself why so many people voted for something we all think is completely stupid.
A couple of examples
1)Immigration -
It clearly played the biggest role, why do so many people think immigration is a problem(Even if the all the evidence shows it isn't). Well it could possible have to the with maybe the last essentially liberal coalition government(Cameron tories idealises Blair by the way) constantly using racism and xenophobia to bait people in voting for them - the immigration vans or maybe we could go back further to when New Labour were pushing racism and xenophobia - ''British Jobs for British People'' to quote Gordon Brown.
Let's not forget the BNP in 2009 European election got almost 1 million votes, the racist and xenophobic vote had been on the rise long before Brexit.
The infamous Nazi like sign that Leave used showing lines of middle eastern people with the words Breaking Point underneath, why would the British(Well English)public have such a racist view towards people from the middle east - the whole war on terror put forward by the liberals in the 2000's might have something to do with it
2)The economy -
While New Labour had slightly different continuation of the Thatcher era, the slight differences being actual quite important, it was in the end a continuation. When this model failed badly in 2008, the response by coalition government to this failure was to used ''austerity'' as a cover for class war.
So almost 30 odd years of a political and economic consensus that not all destroyed huge part of the UK and left people completely alienated but also try to destroy any idea that there could be a alternative to this consensus(When this alternative came in the form of the movement be hide Corbyn, the far right all the way to the centre left would attack it).
My argument is that the effects of neoliberalism have played a major reason to why Brexit happened and without adding this into the analysis you won't understand why people seemingly voted for something so stupid.