This just occurred to me as a shower thought the other day, but why, in Star Wars, do planets of the Republic during the era of the Old Republic even tolerate the Jedi in the first place? The Jedi are basically wandering "knights errant", right? They go around doing good, righting wrongs, fighting injustice and all that stuff. But from a legal standpoint, whose authority do they get they power to do this from? From the perspective of most people in the galaxy the Jedi just show up (violating planetary sovereignty), start poking their nose around where they aren't wanted, and before long they've stirred up a whole bunch of trouble and there a lot of people dead from lightsaber wounds.
So who gives them the power to go where they want and investigate what they want, especially when their operations so often involve violating planetary independence or resulting in a lot of collateral damage? Are they deputized by the Senate? What do they have jurisdiction over? From the Jedi perspective, they get their authority to intervene from the Force, which is a universal phenomenon (and hence, supercedes planetary authority) that dictates morality that conveniently only they can hear. That isn't going to convince a lot of people. What part of society gives them the legal right to get involved, and who holds them responsible if they make a bad decision (e.g., the Jedi equivalent of police brutality).
I know there's that whole argument that most folks in the galaxy see the Jedi-Sith feud at little more than a religious dispute between sects of the same religion, but this even applies to the Jedi by themselves. There are a lot of cases where the Jedi are invited to solve a problem (e.g., Naboo, Kamino), but what about other times? All the way back in Episode IV one of the first things Obi-Wan does is cut someone's arm off with a lightsaber. Granted that was a random thug in "a wretched hive of scum and villainy" in Hutt space where kill or be killed is the one true rule, but what if that happened in a core world like Corellia or Alderaan? What if someone snapped like Anakin did in a highly public area? Are the Jedi held responsible for their actions? What if one of them falls to the Dark Side, is the Council legally responsible for them? And in Episode II Obi-Wan sneaks onto Geonosis during what is ostensibly peace time before the outbreak of the Clone Wars. Is he violating planetary sovereignty? Or better yet, remember how in Episode III the Jedi tried to arrest Palpatine for the crime of "being a Sith"? I get that was meant to show how corrupt the Jedi Order has become, but it's not that much different from their usual modus operandi.
The other thing is the Jedi are a militant religious order that although they pay lip service to Republic laws are ultimately only bound to their code and beliefs. The closest things I can think of to them might be the Hashishin in the Middle East or the Teutonic Knights in eastern Europe. The same Teutonic Knights, I should mention, who were a major pain to the Polish-Lithuanian Commonwealth because they were a non-governmental superpower who rampaged wherever the heck they liked in the name of their religion (even if the people they were rampaging on were also Christian). And that's not counting the people who would outright see them as the Republic's militant arm or international police force.
Now, I know that on paper the Jedi weren't the military arm of the Senate. They were supposed to be a neutral third party who were the go-to diplomats for disputes because they were known for their non-aggression and they were also very, very hard to kill, preventing someone from ending peace talks by just assassinating them (see: Episode I). But the thing is a lot of people in-universe seemed to treat the Jedi as the Republic's police, to the point that the Jedi Council had to explicitly remind the Senate "uh, you guys know we're not your military, right?"
So, from the average person in the Republic's perspective, the Jedi are a militant religious order with a tendency to engage in civil war, who go wherever they want enforcing their idea of justice despite being beholden to no government or law, have a tendency to pressure their citizens into giving up their children to them, and if one shows up is basically a sign that the Senate is likely to start turning over rocks and uncovering dirty secrets. So why do the planets across the galaxy not start putting up giant "no Jedi allowed" signs?
To be clear, I understand why things are the way they are from a storytelling perspective and admit that this is a bit of a slanted view. I actually like the Jedi as characters, I'm not some crazed Karen Traviss Mando supporter. But my broader question is why in-universe did the planets of the Republic tolerate them so much (or at the very least not ban their vigilante actions)? Especially when they're not privy to the Jedi's motivations like the audience are and don't know they are mostly good guys rather than a non-governmental monastic order with too much power and too little oversight?