Of course nobody speaks for the "climate justice movement" categorically, in the same way as nobody speaks for "conservatism" or "progressiveism" as a movement. But if someone had said in 2008 that ACA was a stepping stone to Medicare for All, would that have been inaccurate?
Putting it another way: I don't think market-oriented environmentalists--for whom averting climate change is a matter of appropriately pricing carbon externalities--are driving the bus of that movement anymore.
Rashida Tlaib supports Scandinavian social democratic policies, and supports this website. But she'd support the social democratic policies either way. I agree with you and not with her (on Scandinavian social policies applied to the US), but her support for this website is not really evidence for it being representative of the mainstream; Tlaib is herself not even representative of the mainstream of her own party. That's why they call her, Omar, and AOC "the Squad".
So to rephrase my question: do you really believe the majority of people who believe we should make tradeoffs in our economy to favor combating climate change also believe in the nonsense in this People's Demands site? Because that's what you sort of directly implied.
The economies in non-western countries aren't any different, often just less perfect versions of western market economies. (And sometimes, like with Taiwan or Singapore, more perfect versions.) The important point there, though, is that even imperfect market economies have led to enormous increases in prosperity for non-western countries. Market reforms in countries like India meant that GDP per capita more than quadrupled from 1999-2019, while it less than doubled from 1979-1999.
The climate justice folks, by contrast, want people from the developing world to rely on "endogenous and indigenous technologies and innovations in addressing climate change" so they can "develop, access, and transfer environmentally sound, socially acceptable, gender responsive and equitable climate technologies." https://www.peoplesdemands.org. (Luckily, countries like India are going with Thorium reactors instead: http://large.stanford.edu/courses/2018/ph241/wolak1. And that will be the ironic outcome of climate justice efforts. It will be essential to get India and China on board to address climate change, but those countries are too smart to jump on that bandwagon.)
Ironically, it is precisely the dichotomy you mention that justifies the hard-line opposition of the right-wingers. If tweaking market economies is not the solution, and the alternative to the status quo is "revolution," then it is utterly rational to seek to protect the status quo.