“We had dolls for all types of families — lesbian moms, a heterosexual couple, a single mother, divorced parents,” said Parral, a 45-year-old Valencia art teacher who staged the show with his husband. For students 12 and up, Parral has given diversity lessons in public schools that invite boys to paint their nails while girls draw beards on their faces.

“The idea is to explore gender as a cultural construct,” he said.

That kind of inclusivity is now in the sights of Vox — a far-right party that could be propelled into the national government for the first time as a result of Sunday’s elections. While Vox isn’t expected to come in first or even second, polls suggest it could be the kingmaker for the far larger center-right Popular Party (PP).

An alliance between the two would give Spain its most conservative government since the death of its longtime dictator, Gen. Francisco Franco, in 1975. It would dramatically swing the pendulum in a country that has become an unlikely bastion of progressiveness. It could also noticeably shift the political balance in Europe, where a more fervent brand of conservatism has begun to take hold, challenging forward-leaning positions on everything from gender to global warming.

In Spain, voters from the Canary Islands to Catalonia are going to the polls with the Socialists of Prime Minister Pedro Sánchez and allied parties on the left seeking to fend off a predicted conservative wave. The center-right PP led by Alberto Núñez Feijóo, a 61-year-old Galician, is considered the front-runner, but polls suggest it may have to form an alliance with Vox to govern.

Just as in the United States, classrooms in Spain have become a battleground. Vox has vowed to strip “ideology” from schools, cultivate national pride, let parents decide what books their children read and allow them to skip objectionable lessons.

As Juan Manuel Badenas, a senior Vox official in Valencia, explained it: “What we want is for schools to teach so that children can become good citizens and good professionals, with ideology according to their family and according to their traditions.”

“What they want is to go back to Francoism,” said Pau Vendrell, 43, Parral’s husband. “They want to go back to a time when diversity existed, but you could not speak of it.”

During the Franco era, Spain imposed legal restrictions on women in the workforce and sent homosexuals to camps, prisons and mental hospitals for electroshock treatment. Five decades later — and following five years of left-wing rule — the panorama could not be more different. Children as young as 16 can now change their legally registered gender without medical supervision and obtain an abortion without parental consent. An “only yes means yes” law enshrines explicit sexual consent.

All are measures Vox has vowed to try to repeal.

“Why do activists come and tell things to children that they shouldn’t know? To tell them that they are not a boy or a girl, that they could be something else when it hasn’t even occurred to them to think about it?” said Santiago Abascal, Vox’s national leader, during Wednesday’s debates in denouncing Spain’s new transgender law. “It’s a law that confuses teenagers at the most difficult time in their lives.”

A taste of what could happen under a national coalition of the right can be found in Valencia and other communities where the center-right has struck power-sharing deals with Vox. In one Spanish town, Vox politicians have pulled funding for a play — “Orlando,” the gender-bending work by Virginia Woolf. In another, they have banned nonofficial flags — including the LGBTQ+ rainbow banner — from public buildings.

Natalia Vélez, a mother of two living in a town 50 miles north of Valencia, said she hopes it’s just the beginning of Vox’s house cleaning. She recently sought the advice of Christian Lawyers — a conservative activist group — after students at her 9-year-old son’s school were asked to wear purple ribbons to promote awareness of gender-based violence against women. (Vox argues violence has no gender, so women should not be singled out as victims.) She also objected to a lesson at her son’s school where children were shown a video of a boy who likes to paint his nails.

They say “that it’s normal, that it has to be normalized,” she said. But “it is easy to manipulate children at such a young age.”

The election in Spain highlights how central and similar the culture wars are in Western democracies right now. In Spain, a sweeping victory for conservatives would also come as hard-right parties have gained traction across Europe — including in its three largest nations with dark legacies of right-wing or fascist dictatorships.

The far-right Alternative for Germany party is surging in the European Union’s most populous nation, winning local elections and polling nationwide at double the levels it had a year ago. Italy last year elected its most right-wing government since Benito Mussolini — with Italian Prime Minister Giorgia Meloni, now a rising star on the global stage, this month declaring a new conservative wave washing over Europe.

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“The hour of the patriots has arrived,” Meloni said in a virtual address this month in Spanish to Vox voters in Valencia.

Vox began as — and remains — a party fixated on Spanish nationalism, and it has skewered the socialists for tactical arrangements with Basque and Catalan parties that have agitated for independence. But separatism isn’t such a dominant theme in this election, and polls suggest that despite its regional victories, Vox support nationally has flatlined at around 14 percent.

Yet it could still enter government — and influence the national agenda — through an alliance with the center-right.

Feijóo had previously pledged to try to avoid a deal with Vox — a party that even some members of his PP have dismissed as sexist, homophobic and retrogressive on the settled science of climate change. More recently, though, Feijóo has suggested that his agenda may dovetail with Vox’s in some areas, such as the elimination of Spain’s Equality Ministry.

“It is a surrender to machismo,” Sánchez, whose party is polling second, said during this month’s televised debates.

“They are only thinking about the chance of being in government now,” said Lluis Orriols, a political scientist at Madrid’s Carlos III University.

What would follow any coalition deal would be horse trading between the PP and Vox on cabinet and policy. Some of Vox’s positions, however, remain highly controversial in Spain. Deniers of man-made global warming, Vox officials have pledged to fight “climate delirium” by working to remove Spain from the Paris Accords, eliminate bike lanes and undo water management limitations imposed due to severe droughts.

Spain is baking in a brutal European heat wave that has forced some businesses to curb hours and political parties — including Vox — to reduce campaign events. But Vox politicians have remained unbowed. Their platform includes a pledge to abolish some “meteorological agencies,” and in Valencia, politicians have come out strongly against the creation of a regional climate change agency.

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“I think it’s evident what the risks are” if Vox enters government, said Benito Fuentes, a meteorologist with Spain’s meteorological agency.

“I don’t think they could abolish the agency,” Fuentes said, not speaking for his employer. “But they could reduce staffing, and we would have to prioritize our services … so it’s an indirect way” of curbing climate studies.

The elections are to some extent a highly personal referendum on the photogenic Sánchez, who has been accused of prioritizing self-promotion over governance and was seen as doing poorly against his rival in a recent debate.

But there is also a sense among some in Spain that the socialists are more broadly to blame for their own decline — for bungling some laws while overshooting public opinion on others.

The “yes means yes” law that went into effect in October, for instance, was designed to give rape victims more leverage in legal cases by making the lack of explicit consent a vital factor in determining sexual assault cases. But the law contained language that ended up reducing sentences for hundreds of jailed sex offenders — a loophole that prompted a rewrite, and Sanchez to issue an apology to victims.

In some Spanish regions, left-wing voters are abstaining from voting in significant numbers. Part of the feminist movement has splintered, meanwhile, with a section of it joining the ranks of Harry Potter author J.K. Rowling by expressing outrage against Spain’s new transgender law, which they argue too easily allows biologically born men to enter safe spaces for women.

But Spanish liberals are unlikely to forfeit real ground without a fight.

In Náquera — a town of 6,200, about 17 miles north of Valencia — one of the first acts of the new Vox-dominated local council after May elections was to prohibit nonofficial banners from city hall, including gay flags. Several hundred protesters marched in response.

On a recent visit, a reporter spotted five rainbow flags flying from private balconies within a few blocks of the main square. Activists said those banners, along with roughly 20 more in other parts of town, had mostly sprung up since the new law was passed.

“The effect was the opposite” of what they expected, said Igor Martin, 27, a nursing student and gay activist in Náquera. “There was much more union within the town, and a rallying around people’s freedoms. We’ve known each other all our lives. We know we belong here.”

Beatriz Rios in Brussels and Roser Toll in Barcelona contributed to this report.