Kardashian Fam -- Shocked By Obama Diss

The Kardashian clan says they were completely blindsided when Michelle Obama revealed that Barack doesn't like when their daughters watch their reality show ... insisting the President has them pegged all wrong.

The K-squad is telling friends ... they read Michelle's new interview with iVillage ... in which she said, "Barack really thinks some of the Kardashians -- when they watch that stuff -- he doesn't like that as much."

We're told the Kardashians were "surprised" by the news ... because Obama personally told Khloe he thought "Keeping Up with the Kardashians" was a "great show" when they met last year.

In fact, the Kardashians believe Sasha and Malia could actually LEARN something from the show ... because it features girls in real-life situations facing real-life problems ... health, relationships, the whole gamut.

As for why Khloe was even invited to the White House ... she tagged along with her Lakers star husband Lamar Odom, who was invited to celebrate his 2010 NBA Finals victory.