The Jedi felt the need to politicize their power, thats where their fault lies. The sovereignty of the Republic wasn't being threatened besides the systems that wanted independence. The Jedi werent the private of army of the Republic nor politicans, so they had no say in what was an internal conflict. They felt something was off and fought anyway. Sidious knew the Jedi had too much pride and too arrogant to back down from a fight.