I'm a pragmatic libertarian. I feel right at home with

Black and red because I value the freedom to do what I want, and to accomplish my goals by whatever means are open to me. I throw in green because completely throwing out the pecking order isn't always a good idea. You need a tried and true framework that also gives you room for individualism without the constraints that come from .

Franelity of Order:
Mercykillers:
HarmoniuM:
Transcedent Order:
Athar:
xAositECtS:
bleak cabal:
DOOMGUARD:
Dustmen:
Fated:
Free League:
Revolutianory League:
Sign of One:
Society of Sensation:
Believers_of_the_Source:

I am unfamiliar with all of the above.

I mean, I know what mercy killing is, but I don't think we're talking about the same kind of mercy killing

If you're willing to go just a little square peg/round hole you can actually fairly define the Factions on the monocolors and dual colors

Harmonium - essentially in agreement with you, the Harmonium are monowhite. Total jerks, too.
Sign of One - This is probably our most absolute disagreement. IMO, the Signers fit blue because of their focus on mentalism and mind-over-reality (or mind-is-reality, as the case may be). Both their unique powers and the idea of solipsism seem fairly blue to me.
Fated - I don't think they strictly need green. True, a focus on 'strength' is kind of green but the Fated don't take that at all literally... they're more anarcho-capatilist, plus an active hatred of the very concept of charity, which is pretty wholly philosophically black.
Xaositects - Randomness will do that
Free League - I can get behind your RUG ideal, but the Free League seem green to me because they refuse order without rejecting the idea of order. You want to be an indep? Fine, be an Indep. They aren't quite red, because they do have some collective identity, but it's one that arises from a refusal of artificiality inherent in the other factions and their establishment. In short, they're too communal for red but to anti-order for white.

Fraternity of Order - They basically ARE the Azorius. In fact, with the Planeshift series admitting that the Multiverse can exist in D&D's cosmology, maybe Azor was a Guvner.
Athar - Nihilistic and atheistic, the Athar have thought about it and decided that the Powers of the multiverse are not deserving of worship. I feel like this is a fit for 's intellectualism and focus-on-self rather than a "Greater power"
Revolutionary League - I don't believe that they should qualify as White; their focus is on tearing down order (Because they see the order of the world as it is as corrupt)
Transcendent Order - Essentially, they are the enemy of Blue and Blue's focus on thought. Do not think. Act. Become.
Beleivers of the Source - The transcendence they preach is fairly similar to the Selesnya. I suppose it is more individualistic, but I don't think so much that it NEEDS black

Dustmen - Peace through True Death, they get to sit in the colors of graveyard-exiling. WTB Rest In Peace with alt art and Dustmen watermark. Or Leyline of the Void/Cremate
Mercykillers - Law and stabbing those who disobey it, they're basically the Boros Legion.
Society of Sensation - I think we're on the same wavelength, I just don't see the white in them, compared to the exploration and, well sensation
Bleak Cabal - We're weirdly in agreement; They reject a higher meaning (a green disagreement with White) but strive to forge their own meaning (rather blue) largely through community service (back to green). Signature ability: Madness. Amsuingly enough, I know Madness was a deck at some point.
Doomguard - Now this one I admit being something of a stretch for me, you could call it the short straw of a cycle, but I think I have a cogent argument. (I feel that is dead wrong) is what they do. At least under the likes of Pentar they're destructive weapon merchants, arsonists, and so on. But what do they believe? The only core tenet of Doomguard Philosophy is that everything is breaking down. Everything is decaying. They can't agree whether or not Entropy is progressing too slowly (A majority opinion for the violent psychos), too fast (Discussed in writeups of the Doomguard but rarely seen in main line), or at exactly the pace that needs to and screw BOTH menders and destroyers trying to alter that flow. Decay, and recognizing an inherant flow to and through decay, is a fairly established trait of Black/Green. As opposed to the Golgari, the Doomguard see a one-way line and not a circle, but I don't think you need the circle to qualify as .