Introduction:
It's pretty easy to demonise groups like the Trade Federation, and certainly the Megacorporations of the Galaxy did some deeply immoral things in the years leading up to the Empire... but I don't think it's entirely fair to blame them for what happened. A lot of the focus on sympathetic separatists goes to non-corporate interests, with people like Mina Bonterii and Avi Singh; but I do think it's worth analysing the corporate perspective.
(note: this will be a canon-focused post as I'm going to reference things like The Bad Batch and Star Wars: Brotherhood, because that's what I am more familiar with, but I would welcome the PoV of people who have more familiarity with Legends in the comments, particularly if you know about the Stark hyperspace war, which IIRC was a factor in the old EU)
Droids:
This is a point that I think needs to be addressed early, because a major reason the separatists as a whole, but the corporations in particular, get demonised is their reliance on droids, which are naturally harder to empathise with.
Firstly, that's essentially Organic Chauvinism. We know Droids can be deeply moral individuals with their own outlooks and beliefs, and we have known this since C-2Po and R2-D2 were major characters in 1977. The use of a mechanical army and a mechanical workforce means that it is hard work to empathise with groups like the Techno Union and the Dtrade Federation, but that is work we should put in.
Secondly, it's unfair to demonise the corporations for that, when the Republic explicitly penalised them for NOT hiring droids. Given their druthers, the Trade Federation at least would rather hire Organics, but the Republic passed Legislation that outlawed the use of droids for specific tasks. We only know this was done for certain with Mekneks, but consider: Organics are generally (individual cases vary) cheaper than Droids (Cassian says this explicitly), and in the case of soldiers, organic warfighters are said to be "immensely superior" (take this claim with a grain of salt, though; it is being said as part of a marketing pitch from a de-facto salesperson). Taking all of this together, I think it's fair to assume that the corporate use of droid armies was AT LEAST IN PART the result of Republic regulation.
Taxes:
This, I believe, is the single strongest case for the corporations; the Republic's tax scheme was ABSOLUTELY UNJUST.
There's a very important line in the opening crawl of Episode I that we need to consider:
The taxation of trade routes TO outlying systems is in dispute.
(emphasis mine)
This is crucial to establishing that the Trade Federation had a morally just case for blockading Naboo; the line does not say that the taxation of trade routes FROM outlying systems is in dispute.
The Trade Federation is not questioning the Republic's right to tax cargo that they ship from the Outer Rim to the Core; that is the unambiguous right of a sovereign government to impose tariffs upon imports; when a merchant vessel moves goods to a port, it may be required by the government controlling that port to pay a tariff, tax, toll, burden, or fee. This is entirely justified, as governments must raise revenue to support themselves, and fund the upkeep and protection of such ports.
No, they are questioning the Republic's right to tax cargo that is shipped TO the Outer Rim; and well they should, because the Republic has clearly abandoned the Outer Rim in all but name.
Name, and tax duties.
Shmi tells Padme that "The Republic doesn't exist out here [on Tatooine]", but this is in response to a question about the Republic's anti-slavery laws, which Padme assumes should be in effect on Tatooine. Shmi is describing a practical reality, not a legal one.
Notably, in Dex's Cantina, when Obi-Wan asks if Kamino is in the Republic, Dex responds "No, it's beyond the Outer Rim" (emphasis mine), suggesting that if it were NOT beyond the Outer Rim, it WOULD be in the Republic.
So, by law, Tatooine and other outlying systems are in the Republic, and the Republic taxes trade to them. This is particularly galling as Republic Credits are not even valid tender on Tatooine; local merchants won't accept them, which may be due to the Republic switching to fiat currency as it appears to have decommissioned or isolated all of its mints, with At-Attin being sealed well before the Clone Wars.
Presumably, the Republic still demands that taxes be PAID in Dataries, effectively forcing anyone who wants to engage in interstellar commerce to maintain a reserve of what was effectively a useless currency.
Of course the Trade Federation was upset; anyone would be upset. Starting a blockade as a form of political protest was a reasonable and proportionate response to a Senate policy that amounted to rent-seeking extortion.
Representation:
Yes, it's true that many corporations had representation in the Republic Senate.
This may seem unusual, but we need to take a mental step back and consider what democracy is (at least conceptually) for.
If the purpose of democracy is to ensure that people have a say in the rules they have to live by, and the purpose of Representative Democracy (which includes Parliamentary Republics) is to appoint individuals who will represent the interests of groups of people.
How those groups are selected is, at least in principle, based on shared political interest.
Geography can, to some extent, work as a proxy for political interest; but this assumes people stay in one place for a prolonged period of time.
With the existence of space habitats and ships that people can survive in for a long time, this no longer holds. There are likely large groups of beings who have never even set foot on a planet, born and raised in space, travelling the hyperspace lanes as their profession. No planet or star system can reasonably be said to represent their interests; only the corporations which employ them.
As to how the corporate senators act, I would point out that in Episode I, Lott Dodd doesn't actually defend the invasion of Naboo, and may not even have known about it; he merely asks that Queen Amidala PROVE her serious allegations against the organisations he represents, which is hardly unreasonable.
As to their lobbying during the Clone Wars, it's an unfortunate reality of regulatory states that economic entities will always lobby those with the power to regulate them, because the alternative is to be destroyed by their competitors who certainly will use such methods. It's acompetitive environment, and nobody can afford to fall behind; this has been the case since at least the Palace Economies of the Fertile Crescent. It was true in Ancient Rome, it was True in the Middle Ages, and it is true today. Only in a Lassaiz-Faire system where there is no regulatory authority to Lobby for control over can economic entities afford to stop petitioning for favour.
Yes, Halle Burtoni and Lott Dodd and all the rest of them argued for the war to continue; what else could they reasonably do?
These corporations have employees, creditors, shareholders, and customers to look out for. They have a fiduciary responsibility, and if they fail to maximise profit, they won't meet that responsibility, which means pensions unpaid, wages unraised, and stock dividends unrealised.
Under the circumstances, NOT lobbying for the war to continue would have been a violation of their ethical duties.
Atrocities:
Here comes probably the most controversial part.
It is undeniable that the Separatists, and by extension the corporations that were part of the Separatist alliance, bear some responsibility for atrocities.
However, I think it should be noted that this was at the urging of the Sith, who wanted them to become vilified so that Palpatine could justify nationalising them and seizing their assets (which he notably did to the Banking Clan).
It was also, explicitly, Sidious who ordered that all the Gungans be killed.
Governor Bibble's infamous message was ultimately revealed to be a lie, a trap to lure the Queen back to Naboo; realtively few people died in the Naboo occupation.
So, whilst we can certainly argue that specific individuals within the corporations, such as Nute Gunray, were vindictive and spiteful, I don't think it is fair to judge teh corporations as a whole; any more than the Jedi as a whole are to blame for Pong Krell.
Conclusion:
The narrative heavily criticises the corporations, particularly the Trade Federation. Even some Separatist Characters, such as Ruug Quarnom of Cato Nemodia and at least one member of the Separatist parliament (mr "Unlike the Republic, Corporations do not rule us, ooh lah lah, has anyone seen my Croissant?")
However, I don't think this is entirely fair. The corporations were one part of a vast, broken system, doing their best for the people they had a responsibility to. They were not alone in their sins, and nor were they unique in their complicity; ultimately, they were as much victims of the Sith and of the generally doomed political circumstances as anyone else.