IIRC the premise was that we would carry our nuclear rivalry off world into space as we developed the technology. The possibility of bomb throwing humans flying around the peaceful galaxy was the cause of Klaatu’s angst.
Which is a pretty parochial fear. Spacefaring civilizations would have access to much more dangerous weapons than crude 1950's nukes.
I doubt an advanced civilization would be any more worried about our nukes than we are when we see a chimp using a rock to kill some prey.