I never thought of it like that. Are you saying that on the grand scheme of things "the dark side of the force" at face level by the rest of the galaxy are simply considered a religious sect and not evil, like what would happen if a Jew attempted to assassinate a Mormon who was a senator simply because he was a Mormon?
Wait but hold on, didn't the group attempt to simply arrest him and hold him to trial in accordance with the senate and then he went all sithy on them and killed them all?
I think the important thing to note is that they were absolutely duped by someone evil into doing something incriminating. Windu does open by saying that Palpatine is under arrest, but they do so while igniting their lightsabers with the intent to use them if Palpatine resisted. He makes the "I am the senate" comment because he's telling them outright that if they attack him, it'll be seen as an attack on the Republic. He then forces them to do so while meeting them on equal footing in terms of force, they all have lightsabers and Force skills. From that point on there's no indication anyone isn't fighting to kill there, the fact that the three mook Jedi get murdered in short order doesn't mean they weren't going to kill Palpatine if they could.
The thing is, they attempt to arrest him when they think he's a normal dude, and when he reveals himself to be a Sith Lord properly (which they knew because Anakin told Windu) they try to kill him. When Windu gets the drop on Palpatine (which is almost certainly a feint on his part) Anakin says to him "no, he must stand trial" and Windu argues with him, saying he's too dangerous and controls the courts. Anakin tells him it's not the Jedi way and Windu ignores him and goes to strike, that's when Anakin cuts his arm off and Palpatine blasts him with Unlimehted Powahh.
Pally then plays it off as an "attempt on his life" and uses it as excuse to make himself Emperor of the Galactic Empire. Yes he absolutely orchestrated that situation, but he didn't orchestrate Windu knowingly ignoring his own rules and trying to kill Palpatine because he's a bad dude who needed to be taken out. He only did that because he was a Sith Lord.
As to how much the rest of the galaxy knew about the Sith? Barely at all. In Phantom Menace the Jedi themselves think the Order of the Sith Lords to have been extinct for hundreds of years. The average guy doesn't have a clue, and in the new trilogy Rey thinks even Luke Skywalker was a myth. In A New Hope the Force is so unknown that the moff Vader throttles calls it a "sad devotion to that ancient religion". It's not an important thing in most people's lives, even when they work closely with Force using Sith, let alone someone who's never seen a Force user before. The movies like to pretend that the Force is something everyone is aware of, but I prefer the attitude of the Mandalorians in the Legends canon; that billions die in Jedi/Sith sectarian wars and the galaxy would be better off without both of them. Do I think the average citizen of the Republic understood anything of the real reason Windu wanted to kill Palpatine? Not one bit.