France's far-right National Front leader Marine Le Pen reacts after delivering a speech during the party's annual May Day rally in Paris. REUTERS/Charles Platiau

The rumors started Sunday: President Trump would gut an Obama-era executive order that extends workplace protections to gays and lesbians who work for federal contractors. LGTBQ activists geared up for a fight. But by Tuesday morning, Trump had backed down. In a brief statement, the White House affirmed Trump's commitment to the measure, which covers about 28 million workers.

Progressives celebrated it as a surprise, and a rare bit of good news from an administration run by Mike Pence, who signed a conservative "religious liberty" law in Indiana, supported "conversion therapy" and suggested  that marriage equality would lead to "societal collapse."

But support for gay rights isn't antithetical to a populist, anti-immigrant leader. In fact, it's very much in keeping with the far-right strategy across Europe. In France, the Netherlands and Germany, right-wing leaders have embraced causes such as gay rights and feminism. Islam, they argue, is a threat to the very people protected by these social movements.

It's a smart approach — one that serves to broaden their base. And, as Sasha Polakow-Suransky explained, it's working. She wrote in the Guardian:

They have made a very public break with the symbols of the old right’s past, distancing themselves from skinheads, neo-Nazis and homophobes. They have also deftly co-opted the causes, policies and rhetoric of their opponents. They have sought to outflank the left when it comes to defending a strong welfare state and protecting social benefits that they claim are threatened by an influx of freeloading migrants.

They have effectively claimed the progressive causes of the left – from gay rights to women’s equality and protecting Jews from antisemitism – as their own, by depicting Muslim immigrants as the primary threat to all three groups. As fear of Islam has spread, with their encouragement, they have presented themselves as the only true defenders of western identity and western liberties – the last bulwark protecting a besieged Judeo-Christian civilisation from the barbarians at the gates.

One of the first far-right leaders to do this was Pim Fortuyn, an openly gay Dutch politician with staunchly anti-Islam views. Fortuyn used his sexuality to build his case against Muslim immigration. "In Holland, homosexuality is treated the same way as heterosexuality," he noted at one campaign event. "In what Islamic country does that happen?"

Fortuyn was assassinated in 2002, but others have adopted his approach. In France, for example, the National Front has been labeled the party of racists, anti-Semites and homophobes for decades. Le Pen's father (and former Front head) once called the Holocaust a "detail of history."

When Marine Le Pen (currently running for president of France) took charge, she worked assiduously to change that. Her National Front would appeal to a broader coalition of people, including those in the center and left. It would have to, if it wanted to win. Le Pen purged the party's racist leaders and warned others that that kind of behavior would not be tolerated. Today, Julien Rochedy told the Guardian,  if someone tells a racist joke, "you will be attacked straight away."

"There is such self-discipline these days," he said. "They are so afraid they’ll be accused once again of being antisemitic or racist."

Le Pen has done more than eschew racial language. She has filled her inner circle with openly gay advisers and party leaders. As Le Monde’s Olivier Faye has written, she is "trying to erase another image that has stuck to the skin of the FN — that of homophobia." It has worked: Her share of the vote among married gay couples jumped from 19 percent in 2012 to 32 percent in 2015. That's even more remarkable because Le Pen opposes gay marriage.

The Dutch far-right Party for Freedom has employed a similar strategy. Leader Geert Wilders is staunchly anti-Islam — he speaks often of an "Islamic invasion," in which radicalized teenagers and terrorists would take over the country and turn it into a theocracy. Wilders has proposed an immigration ban, a tax on Muslim women who wear headscarves and a ban on the Koran.

Wilders has been brought up on charges of inciting racial hatred, but his message has resonated with older liberals who helped push an agenda of sexual freedom, feminism and gay rights in the 1960s. These values are now woven into the country's fabric. "Islam is a totalitarian ideology. Muslims are its victims. Just imagine you’re a gay person in a Muslim family," Wilders wrote in one op-ed. "The more Islamic apostates there are, the less misogyny, the less hatred of gays, the less anti-Semitism, the less oppression, the less terror and violence, and the more freedom there will be."

This has left gay people feeling threatened and reflexively suspicious of Muslims. It doesn't help that few Muslims march in gay pride parades. And the Party for Freedom has capitalized. As the Guardian explained: "Among openly gay couples and religious Jews alike, there is a palpable fear of being targeted by homophobic or antisemitic young Muslim men. Much as in France, this fraught atmosphere has made far-right parties seem a palatable option for groups who would never previously have considered voting for them."