Whether you agree with their reasoning or not, it's very normal for countries/nations/states to undergo financial struggles for years immediately following independence.
Did those who voted Yes in the Scottish Referendum believe that they would be instantly richer and living a more privileged lifestyle as soon as they went their own way, or did they expect that it would be a rough old ride to start with, but one that was well worth it for the far greater gains and freedoms that they believed would eventually be theirs as an independent country? Or were they all just 'racist little Scotlanders'?
Some people do believe that temporary - or even permanent - losses of wealth/privilege/opportunity in some areas are a price worth paying for independence and freedom. If you were married to an immensely rich man who provided you with every material and financial benefit that you could possibly desire, but it became clear to you that he despised you, took you for granted and treated you like an employee, would you be 'crazy' for divorcing him, or would you think your independence and self-respect was worth more than all you could keep if you stayed quietly compliant in the gilded cage? They may well have been deceived, but I believe that this is how a huge number of Brexit voters probably felt.
Again, whether you believe that he was telling the truth or not, Farage's proclamation was that he wanted to be 'friends with Europe, trade freely with Europe, but not ruled by Europe'. However achievable this was/is in reality, can you honestly say that this sounds an openly fascist/hateful/racist/incendiary/absurd desire?
Like with the blatant £350m a week bus lie, it's hardly the first time when voters would have made their decision based on 'facts' and promises from their political 'superiors' which turned out to be outright lies.
Until the point when political promises, proclaimed principles and manifestoes are made legally enforceable, with regular independent 'appraisals' and the threat of severe punishment for those who break them or do a sudden about-turn once they're safely elected, what alternative does the average person truly have but to hope that everybody who seeks their vote is not lying through their teeth? I personally blame the liars far, far more than I do those who fell for the lies.