the alter-globalization movement has actually always argued in favour of the types of things that the eu provides and nafta doesn't. for example, full mobility rights. that's one of the things that opponents to nafta have long argued in favour of in order to fix the labour problems in the deal. yet, this was probably the biggest single factor in britain's choice to leave the eu.
brexit was not about fair trade, slave labour or chapter 11 kangaroo courts. it was about immigration.
there's certainly always been a nationalist fringe out there, and the media likes to play into it, but anybody that's been to one of these rallies knows that they get badly marginalized. i've been at free trade protests where people are spending more time yelling at nationalists than they are protesting.
left-wing protesters don't see the issue as a simple disagreement. the nationalists are often associated with crypo-fascist groups like the larouche pac, or outright racist groups. there's a lot of thinking that a lot of them are actually cops, even.
it's a horrible comparison. the right comparison to brexit is to trump, and we need to collectively come to terms with that rather than deny it or try to spin it.
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the relationship between alter-globalization forces and the eu is complex.
on the one hand, the eu is an anti-democratic institution that works for the investor class at the expense of everybody else, and alter-globalization forces know that and have loudly articulated it. on the other hand, it's helped to functionally tear down borders throughout europe.
when something is complex, the diversity of opinions reflect it. but, i think a proper survey process would find that most alter-globalization types would view brexit as a step backwards.