They need not violate Republic laws, as it is their very use of the corrupt Dark Side of the Force that requires us to root them out wherever they make home.
You do not question when we try murderers, or thieves, so why question when we hunt down Sith? Often they are the same people as the other criminals, just with Force Sensitivity. If they can be redeemed, we will do so. If they wish to be arrested, we can abide. But if they decide to fight, we will kill.
Such is the nature of the Jedi. I cannot understand why people seem to think it is OK to use something as innately corrupt and dangerous as the Dark Side. It drains your life and the life of those around you, feeding off your anger and hate - two emotions most species find distasteful. And yet, somehow, we're bad for wanting to rid the galaxy of these people.
You expect those who break the law to be arrested, and the Jedi hold that the law of the Force is to never stray to the path of the Dark Side. While our Archives are incomplete - the Gulag Plague was not kind to any world - we know that it was a single Sith who took down the Old Republic, and it was the Sith who ruin any attempts at government after.
Attempt to study history instead of spouting from a soap box and perhaps you would see the good we do, instead of narrowly trying to protect the rights of Dark Siders to continue to murder, lie and steal for power - physical power, emotional power, political power. Power is what they want. Hatred is what they thrive upon. If those are two things you wish to see more of, so be it. You are entitled to that view.
But a Jedi will not simply allow these people to subvert others as they themselves have been subverted.
And as for Josh - you were willing to let a young Knight take two Dark Siders away from the Order rather than bringing them to the Temple to be monitored. For all you knew they could have simply killed him when you weren't looking and you'd be the fool. Or the fact that you brought a Dark Sider into the Temple on Coruscant. There's always that.
For all the good you did, Josh, you did ill, too. And while I don't think at the time of the vote you deserved to be ousted, you didn't help your case letting said Dark Sider walk away scott-free after bringing him to the heart of our Order. A sad day indeed when a Dark Sider can walk the halls of our Temple with impunity.
TL;DR: As has been the goal of the Jedi throughout history, we are doing our best to root out the corruption of the Dark Side. This shouldn't be something you find distasteful. This shouldn't be something you think wrong. At what point is being a Sith something to aspire to?