Works have meanings beyond their surface-level detail and literal meaning. They also have themes and clear implications. And Idiocracy certainly has those. It has clear undertones of eugenics.

The first is the clear implication that population demographics require active management. In the movie, there was no mass government program to encourage births among those of low intelligence and discourage births among the intelligent. This situation developed entirely naturally through culture acting on its own. A viewer could only conclude that if this horrible future is to be avoided, that we need to start worrying a lot more about who is reproducing in what numbers. We either need government mandates or major cultural initiatives to encourage reproduction among the deserving. Idiocracy never outright endorses eugenics, but the implication is obvious. Writers aren't idiots. They know the clear implications of their work. You don't end up with a political movie that clearly implies the solution is genocide without realizing that's the obvious implication.

The second is the theme that intelligence is something that can be bred or selected for at all through the social stratification we have now. Are those with PhDs really more intelligent, by writ of birth, than those that never graduate high school? Or it mostly about circumstances of birth, opportunities, personal choices, or even neonatal environmental pollutant exposure? Do we have any real evidence that intelligence differences within the species are something that can truly be selected for? Hell, what kind of intelligence are we talking about? Scholastic ability, emotional intelligence, executive reasoning, etc? There are many types of intelligence. And the very idea that the poor and those of lower educational attainment are of genetically lower intelligence is a key eugenics theme.

Yes, Idiocracy never comes right out and explicitly endorses eugenics. But the implications and themes are undeniably pro-eugenics.