the science of radical life extension is extremely new. There hasn't been much time for life extension to become a political cause.

The idea has been around for a long time. 

Winwood Reade, 1872: "Disease will be extirpated; the causes of decay will be removed; immortality will be invented."

George Bernard Shaw, 1921: "Our program is only that the term of human life shall be extended to three hundred years."

F.M. Esfandiary, 1970: "The real revolutionaries of today fight a different battle. They want to be alive in the year 2050 and in the year 20,000 and the year 2,000,000."

A religion can make unfulfilled promises, and still be believed after a thousand years. If the human race thought differently, radical life extension could have been adopted as an ideal and a goal at any time in the history of medicine, and upheld as a goal for however many centuries it took to achieve. But for whatever reasons, the idea did not take hold, and continues to not take hold. 

I certainly think that the scientific and cultural zeitgeist is more promising than ever before, but we're still talking about a minority opinion. The majority of adults are just not interested, and a significant minority will actively oppose a longevity movement. 

In my own opinion, the rise of AI changes everything anyway, because it foreshadows changes far more profound than human longevity. The pre-AI world was one of untold human generations repeating the same cycle of birth and death. It made some sense to say, why settle for lives being cut off in this way? Can we break out of these limits? 

The rise of AI means we now share the world with mercurial nonhuman intelligence, that can certainly assist a human or transhuman agenda if it leans that way, but which will also be capable of replacing us completely. And if the normal response to longevity activism is indifference because the ordinary lifespan is natural and OK, the normal response to AI takeover is going to be, fight the machines, turn them off, so that ordinary human life can go on. 

My prediction is, any movement to stop AI completely and indefinitely will fail, because elites want AI. They want the power it promises, they don't want to lose power to their competitors, and so they will keep pushing ahead, fateful thresholds will be crossed, and AI will be in charge. 

To the extent [leftists, progressives, etc] oppose a world in which anyone can become transhuman, I think it has to do with fears related to eugenics, rather than considerations of wealth, power, or privilege.

To a lot of people, "anyone can become transhuman" will sound like "anyone can become rich". The response to rich people aiming for space colonization or rejuvenation or mind uploading is usually, they should be spending their money on public health or education or infrastructure; not, how can we make outer space or transhumanity available to everyone and not just an elite. 

Again, social-justice transhumanism is a logically possible doctrine, and the more technological daily life becomes, the more it may organically take shape. But in my opinion, it is more likely to be a niche belief, like being a tankie or an anarchist. 

There might not be, but it's not a thing in vacuum, it was coined with political intent and it's tangled with that intent.