Europe’s Americanisation is ongoing. That may well sound paradoxical. So many transatlantic gaps have appeared in the age of Trump. This American president repels many Europeans, and in unprecedented ways. Many on the old continent seek solace in the contrast: perhaps Europe’s hour could be on the horizon? But it’s striking how European debates on issues such as racism and feminism are now so strongly influenced by movements across the Atlantic. In the realm of ideas and campaigning, Europe and the US are drawing closer, not sliding further apart.

This week offered a fantastic moment of transatlantic sharing. Almost simultaneously two events unfolded. At the Golden Globes ceremony in California, the #MeToo movement took centre stage, while many Europeans watched in fascination. Meanwhile in France, Catherine Deneuve and 100 other French women published an article in which they distanced themselves from what they see as the excesses of that same movement. The piece received a lot of attention, much of it critical. Of course, Deneuve’s fame was one reason. She and others pointed to the difficulty of drawing a clear line between “galanterie”, or insistent flirting by men, and abuse. They warned against “puritanism”.

What has been somewhat drowned out in the outcry is that the letter got a lot of pushback in France itself. Similarly, it can hardly be said there is absolute unanimity in the US about the #MeToo movement, even among the liberal-minded. The New York Times ran a piece last week by the American novelist Daphne Merkin, headlined: “Publicly we say MeToo. Privately, we have misgivings”, which made similar arguments to Deneuve’s.

Of course, American cultural influence in Europe goes way back, and grew in the post-1945 period. But by 2005, the historian Tony Judt had spotted important differences between Europe and America that, he believed, pointed to a growing rift. “The presumptively ‘un-American’ values of Europe,” he wrote in his book Postwar, became “the highest common factor in European self-identification”. European puzzlement at America’s fondness for guns, horror at the death penalty and opposition to the Iraq war, as well as support for the European “social model”, whereby the state has a responsibility to shield citizens, are all symptomatic of the perceived gulf in values.

With Donald Trump’s accession, there is now in Germany as in France a growing debate over whether, and how, the transatlantic link can be questioned. Although this concerns mostly makers of foreign policy, the question might also be asked more widely, about such social issues as diversity, the relationship between the state and religion, gender equality and free speech.

At a grassroots level, many young campaigners in Europe take their cue from American progressives

What’s striking, however, is that at a grassroots level, many young campaigners in Europe take their cue from American progressives. That was on display when the Black Lives Matter movement found echoes on the European side of the Atlantic, and when French anti-racism activist Rokhaya Diallo recently found herself at the centre of a row for having spoken of “state racism” in France.

Fifty years on, some parallels might be drawn with what occurred with the 1968 generation: opposition to the Vietnam war on American campuses found echoes in the Paris May uprising, and in how young Germans challenged the assumptions of their parents. As today’s democracies on both sides of the Atlantic are confronted with a new brand of ultra-conservatism and populism, slogans are repeated across borders at the speed of a click, ideas and new thinking wash over geographical boundaries faster than ever.

Globalisation is still very much Americanisation in that sense, and Europe arguably remains the first destination of what flows out of the US, good and bad. The geopolitical concept of “the west” may be fading, but in many ways our European and American worlds have never been more porous and intertwined.

Again, this isn’t to deny there are differences across the Atlantic. American feminism since the 1960s has indeed been different from French feminism – which has often been described as softer, less combative or radical. Racism in the US has a different history to racism in Europe. But we need to beware of simplifications, including about Deneuve, who in 1971 – at a time when abortion was illegal in France – signed a groundbreaking manifesto in which 343 French women declared they’d had abortions, and called for a change in the law.

Europe today is arguably more complex and under more strain than it was even for that 1968 generation. But that does nothing to stop American debates reaching its shores. Christian identity politics and nationalism, in Poland and elsewhere, have been buoyed by Trump and the American far-right. Likewise, American resistance against xenophobia, climate change deniers or unfair global trade serves as an inspiration for campaigners in Europe, who imitate its methods and language.

For all the talk of the death of the west as a space of values-based liberal democracy, it survives as a world of shared battles and civil society campaigning. Those struggles speak to people elsewhere in the world who don’t enjoy the same freedoms.

• Natalie Nougayrède is a Guardian columnist