A lone, radicalized gunman, motivated by extremist teachings, lashed out at innocent civilians in a Buffalo, New York, supermarket in pursuit of an unhinged political agenda. In the end, 13 people were shot and 10 were killed.

Once again, the political agenda was “the great replacement” conspiracy theory, an idea born in the fringes of white supremacist movements that is becoming mainstream in Republican politics.

The theory is based on a lie: Its adherents claim that powerful people behind the scenes, sometimes identified as Jews, are promoting non-white immigration in order to seize political power from a shrinking white majority. It plays on the anxiety of people who are living through demographic or economic change, but there has been no invasion. Immigration has been in sharp decline for five years, and it is at its lowest level in decades, according to the U.S. Census.

Nevertheless, the idea persists, especially in Republican circles. It is a regular feature on Tucker Carlson’s top-rated daily talk show on Fox News, and it has been parroted by Republican officeholders, including Rep. Elise Stefanik of New York, the No. 3 Republican in the U.S. House of Representatives.

Mainers will also be familiar with great replacement rhetoric from prominent Republicans here, including the party’s 2018 U.S. Senate nominee, Eric Brakey, who warned of “mass importation of new voters” by Democrats who want to force socialism on America; former state party vice chair and Waterville Mayor Nick Isgro, who called immigrants “human pawns … (of) global elites,” and former state Rep. Larry Lockman, who called immigrant welcome centers “a war on whites.” This year, Brakey and Lockman are running to return to the Maine Legislature.

According to a recent poll, almost half of Republicans at least somewhat agree with this statement: “There is a group of people in this country who are trying to replace native-born Americans with immigrants who agree with their political views.”

They trade in this idea even though they know that it has found fertile ground in the minds of men who are prone to violence.

It was claimed as motivation by the killer of 20 people in El Paso, Texas, in 2019; 11 people at the Tree of Life Synagogue in Pittsburgh, Pennsylvania, in 2018; the killer of eight in the Mother Emmanuel Baptist Church in Charleston, South Carolina, in 2015; and 51 worshippers in two mosques in New Zealand in 2019.

After other racist massacres, we have asked Republican leaders to repudiate this false and dangerous ideology that is taking root in their party and shun anyone who traffics in it. But they never have, and we don’t expect them to do so now. The state party has attempted to appear more friendly to immigrants this year, opening a “Multicultural Center” in Portland. But the party showed no sign of separating itself from anti-immigration figures like Lockman at the recent party convention.

Apparently, the party needs the white-power extremists, just as it needs anti-immigrant, anti-transgender, anti-vaccination and QAnon elements, who may make up only a minority of the electorate but who provide the party with its energy and enthusiasm at election time.

We expect that Republican Party leaders, candidates and officeholders– who know that there is no such thing as a “great replacement” – will continue to keep their mouths shut about the extremists in their party so that they can ride their enthusiasm to control of Congress, the Blaine House and the state Legislature in November.

They are playing with fire, and we are all at risk.