I had an idea for a short TL recently, about what if the Moon landings really were fake.
Inevitably, as OTL conspiracists fail to realise, it'd be impossible to keep secret a faked moon landing, and within a week of the televised moon landing, the world's press is saturated with details of the fraud.
The Soviet Union, who had been as fooled as everyone else leading up to the launch, and were ready to concede defeat in the Space Race, suddenly become emboldened. The mothballed Soviet moon project is revived, and it is the Soviet flag that first flies on the actual moon, while in the USA NASA gets torn apart by populist rage.