Arnold Kling posed the question. Let’s go further and say these people reprogram themselves to behave like true immortals, rather than sticking with their inherited and earlier evolved biological intuitions.
If we assume monotonicity (and why shouldn’t we?), we can draw inferences from societies with short life expectancies. They are extremely superstitious, willing to entertain tyranny, and hardly libertarian. Try teaching Henry Hazlitt in the Congo. More generally, pending death makes us think of honor, patriotism, and in-group solidarity.
If longer lives move us away from such feelings, yes some immortals would be quite libertarian. That is one direction a tolerant and secular morality can take, but that is hardly the end of the story. Many more immortals would become non-theistic, rational constructivist, cosmopolitan Benthamite modern liberals, much like Matt Yglesias or Brad DeLong. I believe the elasticity of ideological adjustment is greater in this direction. Those views, and the libertarians, would grow in popularity at the expense of the middle, but I doubt if the libertarians would become a majority or even a plurality.
In other words, a society of immortals would become more like…uh…the blogosphere.
Most of all, I would expect more libertarian attitudes toward social issues. Immortals are going to want to try everything, and why not?
Another factor is the declining scarcity of time. I recall, as a kid, seeing a made-for-TV movie about immortals. None of them had plans or homes. They all lived under a bridge, with the bums, and behaved wantonly. They wanted to behave without social constraint, and that meant shedding their reputations and in essence going on the lam. They figured there was always more time to shape up, slip back into a reputation, and run a major corporation. But how did they vote?