ICBM development started decades before moon landing, same in USSR. It’s true that first space rockets were reused ICBMs, but the tech diverged after that. ICBMs use different fuel because they need to be stored for years with full fuel tanks, for quick deployment. There is no such requirement for space rockets. Space rockets are also much more powerful - you could fit dozens or even hundreds of nukes on Saturn V which is impractical - you don’t put all your eggs in a single basket. Saturn V was never intended to be used as an ICBM.