This is an inversion of what really happened. If they were so scared of leftcoms, why did the FBI/CIA use left-communism as a vehicle to disrupt socialist organizing within the US during COINTELPRO, operation CHAOS, etc? Why did they partially bankroll the Frankfurt school through the CCF? (Because it was nonthreatening, and a great tool to split the left.)
Compatibism (between leftcoms and neoliberal imperialists) as a strategy is well-known. Here’s a few resources for you:
https://www.counterpunch.org/2017/06/15/why-the-cia-cares-ab...
https://intellectualhistory.site.ox.ac.uk/article/a-conversa...
https://www.academia.edu/34758095/Cold_War_Comrades_Left_Lib...
When the leftcoms get too old they just repackage them as neoconservatives: https://gwydionwilliams.com/history-and-philosophy/10-1-more...