In reality...knowing the full truth? No, it wasn't. But to the majority of the Empire's subjects and citizens it was a legitimate government in large part because when he proclaimed himself Emperor and seized almost total power Palpatine spun the lie that the Jedi had attempted to overthrow democracy and seize control of the Old Republic, an act of supreme, horrific treachery that necessitated a state of emergency and reorganization of the Republic into an authoritarian Empire to ensure "a safe and secure society." To most citizens, the Emperor was a savior who rescued the decaying Republic from collapse by altering it into a much more powerful and stable regime that guaranteed peace and security under the banner of a ruler for life who had been a trusted and beloved Supreme Chancellor before and during the Clone Wars.
In short, most subjects liked or even loved Palpatine because of his 13 years in elected office before the birth of the Empire. Why wouldn't they? He defeated the Separatists, won the Clone Wars and brought peace and prosperity.