Because the Separatists in the prequels are kind of like Confederates without slavery - and the absence of slavery changes the moral equation of their rebellion a bit.
Not 'kind of'. The name deliberately recalled that conflict (as did that of their opponents, the 'Grand Army').
As far as slavery goes, however, I think both are guilty. The CIS was made up of plutocracies, not democracies, and they employed vast droid armies (though the Republic used droids too, just not militarily). On the Republic side, the clone army are essentially slaves--and while Republic leadership (other than Sidious, obviously) didn't intend for their existence, they certainly didn't let ethics get in the way of using them. If this was the only issue, they'd be morally equivalent.
Then they're just members of a small polity that no longer wanted to be part of a big polity - and it's hard for me to just automatically say "That makes them wrong!"
No one's ever said that. Hell, I'm Québéçois; I'm extensively familiar with exactly that sort of rhetoric of nationalist revendication because the province has had a vigorous (and, on occasion, nearly succesful) seperatist movement for decades. The key difference is the use of violence: it is illegitimate unless the larger polity is itself violent and oppressive. The Revolutionary War was justified because the smaller polities had no representation, because England imposed pernicious practices on the colonies such as the Quartering Act, and because it enforced those policies with political violence against civilians (i.e. the Boston Massacre). The Republic's 'crimes' are bloated, inefficient bureaucracy and corruption--and while those can be legitimate grounds to split off, they are not grounds for aggression unless met with violence, which there is no evidence ever occured in these disputes until CIS began their harrying. The Republic didn't even have a standing army.
If you start calling yourself Queen, and line yourself up with the large polity trying to stomp on the small polity that wants to break off from you, it's not entirely unreasonable for your opponents to regard you as a legitimate target.
1) Amidala didn't 'start calling herself Queen', Naboo has a longstanding tradition of elected monarchs. Her people choose to call her queen. 2) That was the first movie, anyway; the assassination attempt at the beginnig of Clones was against a Senator, an official member of government. I know Vermont has a mild secessionist movement; do you think Bernie Sanders is a legitimate target for assassination? It's all the more ridicoulous in that Amidala was against militarization and for a peaceful solution, despite the repeated attempts on her life, she wasn't lining up to stomp on anybody. Of course, calling it a political assassination might have been a misnomer, since the real reason for the attempts on her life was part of the deal the Seperatist leadership had with Nute Gunray in exchange for the Trade Federation joining up: he had a vendetta against her over his failed illegal invasion of Naboo in the first film, wanted revenge, and the Seperatists obliged--which makes them all criminals.
Well, sure. If you're going to rebel against a galactic superstate defended by superbeings with superpowers, you should undertake a little preparation beforehand.
Which is precisely the point, isn't it? The Seperatists had been plotting violence from the outset. They are the guilty party in a war of aggression.
Again, sure. That's what a revolution is - you attack the current government until it gives up. I'll give you the "public execution" part - they should have simply spontaneously attacked all the government officials in the vicinity.
That's unspeakably barbarous. Modern, democratic states have no business participating in wanton killing. (But, of course, that's part of the problem: CIS wasn't a democracy, but a group of corporate interests. Much like Enron, Lehman Brothers and Morgan Stanley deciding they've had enough of regulators and hiring Blackwater to start attacking government officials.)
Do we even get to see how the conflict started, and who did what to whom?
The conflict started in the movie. "Begun, the Clone Wars have."
Fictitiously yours, Trent Roman