Stargate SG1
O'Neill - Most likely an Independent. Doesn't have much love for the 'holier than thou' type politicians based on his opinion of Kinsey, so that cuts out the christian right from the equation. Probably jumps a lot between candidates and parties. Could also see him abstaining, but then again it's been established that he is smarter than he looks.
Carter - Moderate Democrat.
Jackson - Bleeding heart liberal in the early stages of the show, probably takes a more pragmatic stance as the show progresses, but he generally remains left of centre on the major issues.
Teal'c - (Handwaving the fact that he can't vote). Would abstain since he'd consider all the candidates to be too dishonorable for his liking.
Hammond - Gonna guess Republican and probably a McCain supporter.
Jonas - Hmm... this is a tough one since we sadly never did see a lot of him. Gonna say Independent or possibly Democrat based on his fight for détente back on his homeworld.
Mitchell - Republican. I'm getting the feeling that he's not very far to the right on social issues, so I'm placing him as in the McCain/Huntsman/Romney camp.
Landry - Quite frankly, I'm just not sure.
Vala - Probably wouldn't care enough to vote.
Stargate Atlantis
Weir - Established as being against the proliferation of weapons and an anti-war protestor in her youth. Democrat.
Sheppard - Independent.
McKay - Conservative (or possibly Liberal) home in Canada, Democrat in the US.
Beckett - Lib Dem in the UK, Democrat in the US.
Teyla - Not sure.
Ronon - Abstains.
Ford - Not sure.
Keller - I wanna say Democrat, but I'm not sure why...
Woolsey - Registered Independent.
Stargate Universe
Rush - Conservative in the UK, conservative Democrat in the US.
Young - I'm leaning towards saying Republican. Fiscally conservative, social moderate.
Scott - Republican.
Greer - Probably doesn't vote since I don't see him putting much faith in politicians.
Eli - Probably doesn't bother to go voting, but when he does he votes Dem.
Chloe - Her father was a Senator from California which is a pretty liberal place, so I'm going out on a limb by saying that both she and her father are/were Democrats.
TJ - Could go either way.
Wray - Is homosexual which probably rules out Rick Santorum. I'm gonna say that she is a conservative Democrat, fiscally moderate-conservative/social liberal.
I love this. I never got past Season 1 of Atlantis, but I've watched all the seasons of SGU and SG1.
I support everything you wrote. I have no complaints although I think McKay is a liberal, and you're totally right on Eli. TJ, meh, who cares --she didn't. Agree on Wray as well