It won't. Instead, what will happen is that people will start attaching the mental labels of "Blue" and "Green" to other commenters, based on encounters in such a thread, and these labels will apply everywhere, and consequently distort the discussions and the voting on all topics.
This. I can' tell you how grateful I am that I have no idea about the politics of most posters I'm familiar with.
Perhaps any forum for political discussions here should allow (force?) people to choose a secret identity (i.e., separate nickname) for use only there.
Summary: I propose we somewhat relax our stance on political speech on Less Wrong.
Related: The mind-killer, Mind-killer
A recent series of posts by a well-meaning troll (example) has caused me to re-examine our "no-politics" norm. I believe there has been some unintentional creep from the original intent of Politics is the Mind-Killer. In that article, Eliezer is arguing that discussions here (actually on Overcoming Bias) should not use examples from politics in discussions that are not about politics, since they distract from the lesson. Note the final paragraph:
So, the original intent was not to ban political speech altogether, but to encourage us to come up with less-charged examples where possible. If the subject you're really talking about is politics, and it relates directly to rationality, then you should be able to post about it without getting downvotes strictly because "politics is the mind-killer".
It could be that this drift is less of a community norm than I perceive, and there are just a few folks (myself included) that have taken the original message too far. If so, consider this a message just to those folks such as myself.
Of course, politics would still be off-topic in the comment threads of most posts. There should probably be a special open thread (or another forum) to which drive-by political activists can be directed, instead of simply saying "We don't talk about politics here".
David_Gerard makes a similar point here (though FWIW, I came up with this title independently).