The problem wasn't just the referendum itself, but again in 2019. Corbyn said he had "a neutral stance on Brexit".

https://www.bbc.com/news/election-2019-50530163

The actual referendum was very close, and there was a lot of room for Labour to argue that it wasn't intended to be binding, or at least a Brexit In Name Only. The result was that Labour was creamed and the Tories got a real majority, whereas previously they'd been saddled with UKIP.

Corbyn also failed at the referendum, arriving at a belated and wishy-washy stance, and without compelling Labour to follow it. Had he resigned then, things might have been very different. Instead, he continued to lead Labour in a way that left people confused about where they stood on Brexit when put in the form of a Parliamentary election. Nobody could read the results as anything but "The nation voted strongly for Brexit."

I don't believe that really reflects what voters wanted, but elections are poor tools for sending messages. What they do is put people in office, and the people in office were people strongly for Brexit.

Labour offered another referendum on membership, which none of other parties offered or were in a position to deliver, so the decision to leave could have been overturned if enough people wanted it to. A Labour victory would have given them the chance, regardless of Corbyn's stance.

The Liberal Democrats took an even stronger position, basically ignoring the referendum. But the LibDems are still out in the wilderness, and got very few votes. All they did was to highlight that Labour was not the anti-Brexit party.

The impression I get was that by 2019, Remainers were tired of fighting about it, weren't enamored of Corbyn's version of Labour (Brexit was only part of it), and weren't going to rush over the LibDems.

And that overall, Brexiteers were enthused. Probably for very bad reasons, but they genuinely believed them. As for the original question, they might have been nudged along by some foreign propaganda and targeting, but it wasn't anything that their own leadership wasn't encouraging them to believe.