Republican leaders piled on quickly following the latest outrageous remarks by Steve King, the longtime Iowa congressman and perceived bigot whom the party has been trying, unsuccessfully, to shake off its pant leg for months.

On Wednesday, King offered a defense of sorts of rape and incest, questioning whether, without the historical persistence of those two crimes, “would there be any population of the world left?”

Republican leaders condemned the comments, with Congresswoman Liz Cheney labeling them “appalling and bizarre” and calling for King’s resignation, which has been the party’s official stance on King since he defended white nationalism, again, in January.

But critics warned that the Republican party’s attempts to show one radioactive member the door should not be mistaken for a party-wide purge – or even a serious effort to come to terms with a problem more pervasive than party leaders admit.

“Asking Steve King to resign, but not Donald Trump, is a Republican strategy for normalizing Donald Trump,” wrote Elie Mystal, executive editor of Above the Law, in the Nation on Wednesday.

Whatever stylistic differences there might be between King’s outrageous statements and Trump’s outrageous statements, two developments this month could indicate that the more urgent case for censure is in the White House.

Last week, a mentally ill Florida man who was a super-fan of the president, Cesar Sayoc, was sentenced to 20 years in prison for sending homemade pipe bombs to Trump’s perceived enemies, including Barack Obama, Hillary Clinton, Joe Biden and the financier George Soros.

Days prior, a man suspected of carrying out a mass shooting in El Paso that left 22 people dead was tied to an online manifesto that echoed the language Trump’s reelection campaign has used in thousands of Facebook ads to describe immigration as an “invasion.”

Trump called for a condemnation of bigotry after the El Paso shooting, but the president’s own conduct before and since threatened to undermine that call. A day before the Republicans came down on King, Trump urged a conservative figure with a record of hate speech as long as King’s to run for Congress in Arizona.

Former Major League Baseball pitcher Curt Schilling was fired by ESPN, the sports network, in 2016 for sharing an anti-transgender meme on Facebook, a year after Schilling was suspended for retweeting a meme comparing Muslims to Nazis.

But Schilling is “considering” a run for Congress, he told Arizona news outlets on Tuesday, a report Trump found delightful. “Curt Schilling, a great pitcher and patriot, is considering a run for Congress in Arizona,” Trump wrote. “Terrific!”

If Republicans were serious about cleaning their ranks of hate speech, critics say, they would have to go beyond the White House and into the halls of Congress, where congressman Louie Gohmert of Texas earlier this year framed a massacre in mosques in New Zealand as a misguided reaction to the “controversy” of Islam; where congressman Matt Gaetz claimed a migrant “caravan” had been funded by Soros – before Sayoc mailed Soros a bomb; and where minority leader Kevin McCarthy posted a tweet, later deleted, warning that Soros and others must not be allowed “to BUY this election”.

Republicans would have to go beyond Congress into state legislatures, where West Virginia delegate Eric Porterfield earlier this year said that “the LGBTQ is a modern-day version of the Ku Klux Klan”; and they would have to not overlook Fox News, which promotes the depiction of immigration as an “invasion” and where host Tucker Carlson recently called white supremacy a “hoax”.

Republicans would equally have to review local party leadership, where an association of Republican county chairman in Illinois recently posted an image of four congresswoman of color titled “Jihad squad” with the tagline: “Political jihad is their game, if you don’t agree with their socialist ideology you’re racist.”

The image, which depicted Alexandria Ocasio-Cortez, Ilhan Omar, Ayanna Pressley and Rashida Tlaib, was inspired by yet another Twitter tirade by Trump, who ranted that the four Americans should “go back” to other countries.

Republicans refused to criticize Trump for the racist tweet.

“We’ve seen the far-left throw accusations of racism at everyone,” said the Senate majority leader Mitch McConnell, “anyone who disagrees with them on anything.”