[16] Claremont Institute fellowships have gone to prominent figures on the right such as Laura Ingraham, Ben Shapiro, Mark Levin, Mary Kissel, and Charles C.

[21][22][23] National Review columnist Mona Charen wrote that "Claremont stands out for beclowning itself with this embrace of the smarmy underside of American politics.

"[21] In 2020, Mark Joseph Stern of Slate magazine called the institute "a racist fever swamp with deep connections to the conspiratorial alt-right", citing Posobiec's fellowship and the publication of a 2020 essay by senior fellow John Eastman that questioned Kamala Harris's eligibility for the vice presidency.

Written under a pseudonym, it compared the prospect of conservatives letting Trump lose to Hillary Clinton in the 2016 presidential election with passengers not charging the cockpit of the United Airlines aircraft hijacked by Al-Qaeda in 2001.

[36] During the 2020 COVID-19 pandemic, the institute received between $350,000 and $1 million in federally backed small-business loans from Chain Bridge Bank as part of the Paycheck Protection Program.

"[41] In early January 2021, along with Trump and other advisors, Eastman unsuccessfully attempted to persuade then-vice president Mike Pence to overturn the 2020 presidential election results.

[6][42][43] The details of Eastman's attempt, described in a book by journalists Bob Woodward and Robert Costa, made national headlines in September 2021.

[44] An anonymous former fellow said Eastman's ideas are based on the doctrine of natural rights, which has been a key element of the institute's politics for many years.

Haywood, a far-right extremist, has described the January 6 attacks as an "electoral justice protest" and wrote about his desire to lead as a "warlord" of an "armed patronage network" following the collapse of the United States.

[47] The Guardian described SACR as an "exclusive, men-only fraternal order which aims to replace the US government with an authoritarian 'aligned regime', and which experts say is rooted in extreme Christian nationalism and religious autocracy.

[50] Claremont is a member of the advisory board of Project 2025,[51] a collection of conservative and right-wing policy proposals from the Heritage Foundation to reshape the US federal government and consolidate executive power should the Republican nominee win the 2024 presidential election.

The publication has featured essays by Newt Gingrich, Todd Young, Marco Rubio, Jim Banks, and Tom Cotton.