It was as he basked there in the Caribbean sunshine that Mr. Cummings, one of the architects of the 2016 Brexit campaign, issued his appeal on his blog for “super-talented weirdos” to come and work alongside him at Downing Street. The idea was to shake up a cadre of top officials, often educated at Oxford or Cambridges, that Mr. Cummings considers complacent.

“We need some true wild cards, artists, people who never went to university and fought their way out of an appalling hell hole, ” Mr. Cummings wrote in a post that prompted applications from, among others, Uri Geller, the self-styled magician-psychic famous for bending spoons.

Mr. Geller seems not to have gotten a callback. But Mr. Sabisky, who describes himself on Twitter as a “researcher” and “super-forecaster,” was hired as an adviser in the prime minister’s office.

Then, over the weekend, reports began to surface about his various online postings.

On Mr. Cummings’s blog in 2014, for example, Mr. Sabisky suggested forced “universal uptake of long-term contraception at the onset of puberty” for what he called the “underclass.”

“Vaccination laws give it a precedent, I would argue,” Mr. Sabisky wrote.

In a Twitter post last May, he wrote that “women’s sport is more comparable to the Paralympics than it is to men’s.”

And in a separate blog post, he said that when it came to “intellectual disability,” there were greater diagnostic rates for black Americans than white ones.

On Monday, Scotland’s first minister, Nicola Sturgeon, appealed to the government to “get a grip fast and demonstrate some basic but fundamental values.”