They were incredibly, fiercely loyal.
Take a look into our own history and look into the SS, the Schutzstaffel. They started as the guards responsible for protecting Hitler and the higher ups, and ended up growing into something...bigger.
The SS-Totenkopfverbände were responsible for running the concentration camp system, perhaps the largest war crime in history.
The SS-Verfügungstruppe operated specifically at the orders of Hitler, and following the Führerprinzip, they were incredibly loyal to Hitler.
The Waffen-SS were the military arm of the SS as part of the Wehrmacht, with the most infamous being the 1st SS Panzer Division "Leibstandarte SS Adolf Hitler." Named after their dear leader, the 1st SS Panzer was completely populated by the most completely loyal soldiers to the Nazi party.
With an entire country to pick from, and decades of time available to hand picking and training and indoctrinating the SS, the Nazis had a fiercely loyal group of men, willing to die at the Führer's orders, willing to do anything for the Fatherland. No war crime was too dirty, no task too deadly, no suicide mission too grim for these men. They were responsible for the Holocaust, and for the equivalent liquidation of Soviets, without question.
And they did all this without The Force.
With an entire galaxy of troops, and decades to hand pick his guards...Palpatine could certainly make an equivalently loyal set of guards; with the Force as his ally, he'd be able to actually detect and quantify their loyalty, and weed out any who didn't match up to snuff. He certainly could have Force-Brainwashed them...but the problem with brainwashed people is that they don't function 100%. What you need are indoctrinated cultists; people so deep into the Kool-Aid that they are willing to ignore anything out of their imposed worldview, to worship a single man, and to accept anything he does as morally right and lawful.
...sadly, it's not that hard to do it.
I don't know of anything in canon to support this, but I've recently read a book in Legends to support this. In Specter of the Past, we meet up with Grodin Tierce, the clone of a Royal Guardsman. The clone says this about the Royal Guards:
A Royal Guardsman never seeks special privileges, ever. His entire goal in life is to serve the Emperor, and the New Order he created. This is his goal in life, and his desire in death.