Imagine a man who voted to leave the European Economic Community in 1975. A man who spoke out against the Maastricht Treaty in 1993, saying that it “takes away from national parliaments the power to set economic policy and hands it over to an unelected set of bankers”. A man who voted against the Lisbon Treaty in 2008.

You don’t have to imagine very hard, because that man is Jeremy Corbyn. When campaigning for the Labour leadership in 2015, he told a GMB hustings, “I would ­advocate a No vote if we are going to get an imposition of free-market policies across Europe.”

When Labour’s Brexiteers gathered to launch their campaign in 2016, several seemed hurt that Corbyn and his shadow chancellor, John McDonnell, were not there with them. “It is surprising, when we voted against the advice of the chief whip on a number of European issues over the last decades, that Jeremy and John, who have always been in that lobby with us, that they would want to lead a campaign that isn’t even asking for a renegotiated position,” said the MP Graham Stringer.

I mention this because since the election campaign started in April, I keep having an odd experience – people insisting that Corbyn is not a Eurosceptic, and that he will use Labour’s new-found strength to argue for a softer Brexit. Others claim that Labour’s current position on freedom of movement (ending it) is the obvious, common-sense – even progressive – choice.

This matters. Look, if the evidence above doesn’t convince you that the Labour leader is intensely relaxed about exiting the European Union, I don’t know what else would. Yet it’s clear that some Labour activists strongly identify personally with Corbyn: they find it hard to believe that he holds different opinions from them.

The second factor is the remaking of Brexit as a culture war, where to say that someone is a Eurosceptic is seen as a kind of slur. Perhaps without realising it, some on the left do associate Euroscepticism with Little Englanderism or even flat-out racism, and see it as a moral failing rather than a political position.

But I’m not impugning Jeremy Corbyn’s character or morals by saying that he is an instinctive Brexiteer. He comes from a tradition on the left that sees the EU as a capitalist club. You can disagree with that premise but it’s a respectable line of reasoning.

Also, the Euroscepticism of Corbyn and his allies will undoubtedly give them an advantage in the months ahead; they are not consumed by fatalism, and the members of McDonnell’s shadow Treasury team feel that the removal of European state aid restrictions can help revive ailing bits of the British economy. They have a vision of what an ideal “Labour Brexit” would be – and it’s not just sobbing and begging Emmanuel Macron and Angela Merkel to take us back.

We do, however, need a reality check. Now that the necessary humble pie has been eaten, Labour’s unexpected revival at the ballot box means we can begin to treat Corbyn as a normal politician – with the emphasis on the second word. He’s not the Messiah, but he’s not a joke either. He is a charismatic campaigner who is willing to compromise on second-tier issues to achieve his main objectives.

From the general election, we can see just how good a campaigner Corbyn is: he can fire up a crowd, give disciplined answers to interviewers and chat amiably on a sofa. That throws into sharp relief just how limp his performances were last year.

He might have little else in common with Theresa May, but they both looked at the EU referendum and thought: yeah, I’m going to sit this one out. He called on activists to accept the EU “warts and all”; and said he was “seven, or seven and a half” out of ten in favour of staying in it.

For both leaders, this was a pragmatic decision. May did not want to be overtly disloyal to David Cameron, but neither did she wish to risk her career if the result went the other way.

Anyone in Labour would have been equally sane to look north of the border and back to 2014, and remember just how much credibility the party immolated by sharing stages with the Conservatives and allowing itself to be seen as the establishment. By limiting his involvement in the Remain campaign and whipping his MPs to trigger Article 50, Corbyn ended up with a fudge that gave Labour some cover in heavily pro-Brexit regions of the country.

That’s the politics, but what about the principle? I can’t shake the feeling that if Corbyn campaigned as hard for Remain in 2016 as he did for Labour in 2017, we would still be members of the European Union. And that matters to me, as much as left-wing policies or a change in the rhetoric around migrants and welfare claimants, because I think leaving the EU is going to make us poorer and meaner.

That’s why I worry that many of my friends, and the activists I talk to, are about to be disappointed, after waiting and waiting for Labour to start making the case for a softer Brexit and for the single market being more important than border controls. As Michael Chessum, a long-standing Momentum organiser, wrote on the New Statesman website, “Recognising the fact that immigration enriches society is all very well, but that narrative is inevitably undermined if you then choose to abolish the best policy for allowing immigration to happen.”

Labour’s success on 8 June was driven by its ambiguous stance on Brexit. To Leavers, it could wink at ending freedom of movement when they worried about immigration; to Remainers, it offered a critique of the immigrant-bashing rhetoric of recent times. But can that coalition hold as the true shape of Brexit solidifies? Over the next few months, Jeremy Corbyn’s biggest decision will be this: which half of my voters should I disappoint?