It’s been fascinating to look at some of the reactions, in Europe and beyond, after the European commission last week took the unprecedented step of triggering a mechanism against Poland, for the first time potentially threatening to strip a member state of its voting rights in the club.

Brussels decided to move against Poland’s democratic backsliding, namely the crushing of its independent judiciary – a process that had recently been accelerated by its populist government, elected in 2015. On social media, the far right raged. Here was the European behemoth lashing out at a country whose sovereign choices were being trampled on, its image unfairly tarnished. Sound familiar?

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In Brexit Britain, Leave.eu on Twitter urged Theresa May to block the “EU bullying of Poland”, “tell the EU get stuffed” and “honour the alliance forged by the heroic sacrifice of Polish airmen in the defence of our country” – with hashtags “WWII” and “battle of Britain”.

Reading comments online, some of them from American sympathisers, I was also reminded of how Donald Trump had waxed lyrical about Poland’s government on his visit to Warsaw last summer: a nationalist US president fawning over a nationalist Polish government with heaps of scorn piled on the European project along the way.

The far right’s take on Poland, very much on display these days, pictures a nation valiantly resisting a “civilisational” threat to the west in which white, Christian identity risks being swamped by Muslim immigration, orchestrated by the EU. In Hungary, the prime minister Viktor Orbán, a self-avowed champion of “illiberal democracy”, declared an “attack on Poland” would be “an attack on central Europe”. He is keen to capitalise on anything that makes his own problems within the EU appear shared.

It matters little that none of this bears any connection to the EU commission’s actual decision last week. Brussels’ move focused solely on the need to preserve independent courts and judges as a key pillar of EU membership. It had nothing to do with migration quotas. Talk of a “nuclear option” being used against Poland is an exaggeration. It’s true the EU has entered uncharted waters, but rules of unanimity will probably protect Poland from further consequences, whether on voting rights or access to European funds.

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France’s Front National, whose leader Marine Le Pen had taken part, days earlier, in a gathering of European far-right leaders in Prague, lambasted “a scandalous decision” that “yet threatens countries who dare confront the absolutism of the EU”. “Today Poland, tomorrow Hungary and then Austria,” she added.

It is perhaps not surprising that Poland’s travails now serve as a rallying cry for forces that hoped the EU would ultimately disintegrate after Brexit. But such pronouncements cannot be brushed aside simply because they emanate from vile parts of the political spectrum. Let’s face it, the EU’s case may seem obvious to the convinced, but it certainly isn’t as obvious to all, including on the left. Remember how Brussels came under fire for turning a blind eye to the Spanish police’s crackdown on Catalan dissent in October, and the imprisonment of pro-independence politicians (an issue that is unlikely to go away after last week’s Catalan elections). And what about how asylum seekers are kept in atrocious conditions on Greek islands?

One can draw up a long list of European countries that fall short of the standards the club is meant to enshrine. Why – some may ask – take steps against Poland’s government when others appear to be let off the hook?

The answer to this has to do with the way the EU functions. Admittedly, that is not something its citizens are often made aware of. The commission is the guardian of the treaties. It is not a human rights monitoring body. That specific task is carried out by other institutions, such as the Council of Europe. As Heather Grabbe, from Open Society Foundations, put it to me: “Rule of law is both a question of values and a foundation of the EU. Without it you simply don’t have the ground on which the single market can work.”

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The commission isn’t just criticising the Polish government for its behaviour. It is trying to preserve a body of European law that concerns all European citizens without exception. Indeed if Brussels doesn’t draw a line here, you might end up with a situation where, say, a German or a Portuguese national living in or visiting Poland, or a business person investing there, will one day find themselves confronted with a politically controlled judge, not a fair and independent one. Much would start to unravel.

Protecting the “integrity” of the single market is likewise an important reason why Britain, as it negotiates its way out of the EU, cannot hope to carve out piecemeal exceptions. Yes, this Polish episode does concern Britain – only not in the way hardline Brexiters think. The commission’s move looks purely political, but it is in fact much more pragmatic than meets the eye. It is not about punishing Poland. It is about the EU’s self-preservation as an economic and trading bloc as much as it is about upholding democratic principles. Hungary, for all its flaws, has to date not crossed the same red lines. Its government, and the new Austrian one perhaps, will now be on notice that if it does, there will be consequences.

However, this latest chapter of EU disputes does raise a problem. To prevent the “double standard” narrative taking hold, more forceful explanations of why the EU acts as it does, or sometimes doesn’t act, need to be made. To judge by many comments so far, we still have a long way to go.

• Natalie Nougayrède is a columnist, leader writer and foreign affairs commentator for the Guardian