It was a fear of power, as everyone pretty much explained. Basically, Palpatine and his supporters (and even just the common folk) felt that the Jedi Order was just too powerful. They could wield a power few understood, they were militaristic, secretive, lived by a strict code, sent emissaries to other worlds to snatch up Force-sensitive children just as soon as the child even began to demonstrate some proclivity to the Force, refuse to return the child if the parents suddenly decided that they would rather their offspring be a layperson, and in many a case, if some civilians were even working at the Temple and their child was inducted into the Order, that employee would be dismissed and barred from seeing their child again. It was mainly the practice of sequestering children from their parents in some arcane order that drove the opinions of civilians.
But to Palpatine, it was power. The Jedi were powerful and he knew it. They became wise to his schemes, they were a clear threat to him and his goals of galactic control. Thus, they must be stopped. And the sure-fire way to stop them was to out right destroy them. Remove the Jedi, remove the threat, remove the power.