I think this is an interesting point, OP.
For a lot of pro-Brexiters, what their view came down to most fundamentally was that certain powers and democratic responsibility belongs, and perhaps can only really be maintained, at the level of the nation state (or lower.) Super-national institutions, though they might have important uses, are simply not democratic institutions in the same way, much less responsive to grass roots viewpoints or "the people". They represent a further abstraction of the political process.
I do actually think that for some people, concerned about GI, seeing how GI has been influenced/worked at the EU level, has given them a sense of what some of the anti-EU sentiment was really about.
And actually, I would say that FWR overall is much more likely to be sympathetic to EU-skepticism than the rest of MN, rather than taking a reactionary stance.
That being said, membership to the EU is a really complicated question, it's very multifaceted with both important principles, pragmatic elements, questions about how it will actually play out, and many unknowns with regards to what other countries will do or what the future holds. So there are many other issues people might consider relevant than just how GI and such play out in the EU.