1) Keep them to myself most of the time. Pick my spots, in other words, and don't just toss off quick replies every time I disagree (who's got that kind of time anyway).
2) Don't make a factual claim without a link to back it up, even (maybe especially) if it's something everyone knows. There seems to be enough respect for the process of researching something and backing up your claims here, that people are less likely to downvote a fact they don't like to hear if you make the effort. (This is one thing that distinguishes HN from Reddit.)
3) Make the case dryly and impersonally. People are less likely to be triggered by disagreement if they don't feel like you're laughing at them or calling them stupid.
4) Include a "to be fair" balancing point if you can do so truthfully. For instance, if you're criticizing the Democrats, point out where the Republicans are also wrong on something.
Of course, none of this would be necessary to keep my karma positive if I were left-leaning, but that's okay. Communities should be allowed to lean whichever way they want, and there's nothing wrong with dissenters having to work harder to fit in.