Leonard Peikoff is urging Objectivists to vote Democratic. Actually, urging isn't the right word. If you consider voting Republican or abstaining from voting, you don't understand Objectivism and may well be "immoral." I guess he doesn't call himself Rand's "intellectual heir" for nothing.
Peikoff is so worried about the influence of the Religious Right (RR) on the Republican Party that he thinks voting Democratic is the only way to stop it.
A few comments:
First, whether to vote for the Democrats to stop the Republicans is obviously a question of strategy and it assumes something that Peikoff hasn't shown (that the Religious Right is incredibly influential). An Objectivist might plausibly argue that even if Peikoff is correct, we are better off with a Democratic house and a Republican Senate.
Second, Peikoff is wrong about the influence of the RR. Outside the South, the Midwest and parts of the West, the RR isn't particularly influential. And in the two largest states, New York and California, the RR has next to no influence (particularly in New York). In virtually all parts of the US, the influence of religion is less now than in the 1950's. If people weren't complaining about the threat of a theocracy in 1956, why are they in 2006?
Third, that some Republicans may be bad doesn't mean people shouldn't vote for "good" Republicans. In local and state elections, there is every reason to vote for the best candidate even if one accepts Peikoff's view about the influence of the RR.
Fourth, this article is typical Peikoff. As David Ramsay Steele once put it, if Peikoff has seriously wrestled with a philosophical question since graduate school, it doesn't show.
Fifth, if an Objectivist can in good conscience vote for a socialist running as a Democrat, by what principle does it become immoral to vote libertarian or not to vote?