Long story short, it feels like it's going to be a different case for lots of places
Yeah, that's probably fair. It just seems odd to me when the books, movies, shows, etc make the Jedi out to be these heroic figures admired, though usually secretly, by seemingly every non-Imperial everywhere in the galaxy. How often do you see characters denouncing the Jedi for there part in the rise of Empire? Even on worlds that held Jedi sympathies before the Clone Wars, it seems that they would be held, at least as an organization if not as individuals, in fairly low regard after the attempted coup.
I would contest your assertion that the Clone Wars caused billions of casualties.
Okay, fair enough. To the best of my knowledge there haven't been any canonical mentions of casualty reports from the war, so the best we can really do is speculate.
The initial order of clones (to my knowledge, we have no concrete numbers for follow-on batches, or clones from other sources, i.e. Spaarti) from Kamino was 3 million.
From a reddit discussion found here. "If a "unit" were to be referring to one of the battalions of 576 troopers (seen on Coruscant), then 200,000 of these would render 115,200,000 clones and the 1,000,000 others spoken of as 576,000,000. This grand total of 691,200,000 would be far more suitable for the core of a galactic army." While it's certainly not from an official source, the reasoning seems sound. Please also refer to the "Command structure of regular forces" section of the Grand Army of the Republic entry on Wookieepedia here, though the source used to arrive at that number is now non-cannon, so I'm not sure how much stock should be put in it.
So that should give us a decent idea of the number of Republic clone troopers, to say nothing of the number of non-clone elements incorporated into the army. It also doesn't address the number of support personnel needed to maintain the GAR. We can guess at this number by using a modern tooth to tail ratio of 1:2.5 (see Quora discussion here), but there's no way to know if that's representative of armies in the Star Wars galaxy. So either way we're left guessing, but let's make some conservative guesses with what we do know.
Let's really low-ball it say that for every 10 clone troopers there is one living non-clone soldier. So with around 700,000,000 clones forming the core the army (please see above) that means there are 70,000,000 non-clone soldiers for around 770,000,000 soldier. Let's also assume that the support infrastructure used to supply the GAR is extraordinarily efficient (it is a sci-fi setting after all), so 10 soldiers can be supported by one living person. That's 77,000,000 support personnel. So the total size of the GAR weighs in at around 847,000,000 personnel.
The clone army, while smaller, was better equipped, better led, and generally more effective on the field of battle (and in naval engagements).
That does seem to be the case based on what we see in the movies, books, etc so let's roll with it. How many battle droids do you suppose the CIS had to field in order to make the war last the three years it did? Maybe 2 for every 1 Republic soldier? Maybe 10? I dunno, let's make another conservative estimate and say it's a 2:1 ratio. That would mean there with around 1,694,000,000 battle droids fielded by the CIS during the Clone Wars.
Add to that the fact that almost no engagements were fought on Core Worlds or heavily-populated worlds and I have trouble understanding where you're coming up with "billions" of casualties. Many hundreds of thousands of clones, a few thousand Republic citizens of various species, several million-plus battle droids, and thousands of Geonosians, Trandoshans, Neimodeans, etc., yes, sure. Billions, no.
So for the sake of discussion I'll grant that most of the Clone Wars were fought away from civilian populations and the casualties inflicted on the CIS forces would be overwhelming non-living anyway and don't count. We could probably argue for a number of exceptions, but let's keep things simple and in favor of your position.
The casualty rate in armed conflicts has fluctuated considerably over the course of recorded history and there are a number of factors at play in a sci-fi setting that we can't really account for. However, let's at least make an attempt at finding a number using modern conflicts as a model (see Quora article here). If we take the casualty rate of the 2003 invasion of Iraq at about 2% and assume that half of those casualties are non-fatal, that leaves us with only a 1% casualty rate. Mind you, we're comparing a conflict that lasted about 21 days to one that lasted 3 years, but modern conflicts after 1945 have been fairly brief and we don't have space ships or laser swords so please bear with me.
At 847,000,000 personnel strong, with a 1% fatality rate, the GAR would have had about 8,470,000 dead soldiers. That's just the GAR. If we could take into account the CIS personnel and civilians killed in battles and the people on each side who died as a result of destroyed infrastructure and/or disrupted supply lines, I image we'd have a significantly higher number. Even without counting them we've got several million dead as a direct result of the Clone Wars.
So all that being said, do you suppose that the minimum 8.47 million corpses laying at the Jedi's feet would shift public opinion against them in the years following the conflict they appear to have started?
The Jedi and the Force are a rallying point for the rebellion, who already know the Empire is bad.
If you accept the premise that the actions of the Jedi directly lead to the reformation of a previously democratic (though arguably pretty ineffectual) government into a totalitarian regime, does using them as a rallying point really make a whole lot of sense? Remember, no one living in the Star Wars galaxy has seen a Star Wars movie. No one knows anything about the Sith, Palpatine's ties to them, their various machinations, etc. They just know what they experience in their lives and what they see on the (later Empire controlled) news. So if you're founding an organization in response to a shift in the government, why would you use the people who were responsible for that shift as your mascots? It strikes me as a bit odd.