don't remember Larry as being as outspokenly political as Jerry (who'd had some professional involvement in politics, including for RW LA mayor Sam Yorty), I'd always assumed he probably shared Jerry's views. Which were very much on display in their 1977 bestseller, Lucifer's Hammer:
https://www.thedailybeast.com/from-lucifers-hammer-to-newts-moon-base-to-donalds-wallthe-sci-fi-roots-of-the-far-right
Archive page at https://archive.ph/Mntxj
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In partnership with Niven, Pournelles science-fiction married aggressive military might with Atlas Shrugged-style techno-futurist fantasies and nativist paranoia, offering what in retrospect looks like an uncannily prescient portrait of the Trump era and its cultural overtones. Take, for example, the pairs Hugo-nominated 1977 novel Lucifers Hammer, which depicts a small ranch of patriotic American farmers as they struggle to survive after a comet hits earth. Early on, the farmers debate how to keep out undesirables:
They'll all be here, all that can get here," Christopher shouted. Los Angeles, and the San Joaquin, and what's left of San Francisco
How long can we keep it up, lettin' those people come here?
"Be n**gers too," someone shouted from the floor. He looked self-consciously at two black faces at the end of the room. "Okay, sorryno. I'm not sorry. Lucius, you own land. You work it. But city n**gers, whining about equalityyou don't want 'em either!"
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This kind of scene the asterisks are mine; they spelled the word out plays on the same fears Trump stoked in his campaign of immigrants and undesirables invading the real America. Yet Pournelle and Niven yoked this divisiveness to an Ayn Randian view of technological progress, in which there are those who work and those who leech.
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Much more about that novel at the links. The article also mentions the quote from Larry that's in your OP.
Jerry was born in Louisiana. I have vague memories of having once read or heard that he'd been leftwing when young and then did the political flip some people with authoritarian tendencies do, but I didn't find anything just now on Google to back that up. (Sam Yorty, whom he worked for briefly, had been a liberal Democrat when young and turned jnto a RW populist before Jerry worked for him.) I don't have any idea where Larry's political views and racism might've come from. He's from a very wealthy California family (his great-grandfather was an oil tycoon), and he sold his first science fiction story soon after graduating from college, though I don't know when he started making enough money on it that he could have supported himself as a writer...or been able to afford insurance if his family hadn't been wealthy.