You might be correct that we won't change the climate on earth so much we couldn't adapt somehow, there's some reason to believe that. But attainable extraterrestrial colonization isn't one of them and probably won't be in our lifetimes.
Also, it's far from guaranteed that we won't change the climate on earth so much it disrupts processes we rely on and possibly decimates the current population from production/supply issues.
There are continually-occupied bases in Antarctica (https://en.wikipedia.org/wiki/Amundsen%E2%80%93Scott_South_P...) but they don't perform any function besides scientific inquiry. NASA has sent people to the moon and back multiple times with 1960s technology, multiple independent entities have sent cargo to the moon, and there have been people living in orbit on the ISS for a while now. We even have oil rigs out in the middle of the ocean.
Nobody lives in any of these places permanently but as far as I know there's no technical reason they can't. It sure seems like if humans set their mind to it there could absolutely be bases or even cities on the moon (I don't know about Mars) with roughly current technology. The reason it isn't happening is that there is no real incentive compared to the costs required. That's why in lots of science fiction the moon has fuel for fusion or something. We know that we probably can colonize the moon, but it's an easy shorthand to explain why we'd bother.
Contemporary hunter-gatherer societies exist, and probably will as long as the climates sustaining them last and the rest of humanity leaves the ranges involved alone. That's probably a good floor for consideration.
Every other society else exists on a scale of autarky to interdependence but given that globalization is fairly recent it seems fairly clear a lot of nation-state scale and maybe smaller societies probably could do agriculture + craft and maybe even industry well enough to be self-sustaining, if perhaps less efficiently or wealthily (Amish / Mennonite communities seem like they'd have a good shot).
Industrialization and interdependence are definitely associated, but we know we can get there from a much more independent place if given environments like those humanity has had (so far) to launch from.
Without a sufficiently friendly environment, we're talking about a different class of dependence (arguably complete). There are harsh environments on earth that demonstrate this, and every extraterrestrial destination available to us makes those harsh earthly environments look like easy mode.
They walk around, outside, with heavy coats, and don't die after 10 minutes. There are PBS videos on YT about how they manage the sewage and garbage in Antarctica, and you can see the guys walking around outside, hanging out.
> NASA has sent people to the moon and back multiple times with 1960s technology
NASA has sent people to the moon, who walked, briefly, while in suits to keep them alive on a minute-to-minute basis. If a single thing went wrong they would die. Several folks almost died -- they made a movie about that -- and some actually died (e.g. Challenger, Soviet losses, etc.).
> multiple independent entities have sent cargo to the moon
in trivial quantities, and where, in most cases, it stayed there.
> and there have been people living in orbit on the ISS for a while now
If by people you mean < 12 humans at a time, and at what is an insanely high expense compared to keeping someone alive in the Arctic or Antarctic. And most of them have major or permanent changes to their bodies, like vision, loss of bone density, or the myriad issues that the guy -- the one (1) guy, who did it once -- who stayed up for a year. An explanation of those health issues: https://time.com/5568522/kelly-twins-year-in-space/ There is no reason to think we could successfully have kids, mature to adulthood, and function as a human in less than Earth's gravity -- and given the impact of micro-grav on adults it's not crazy to think it would be a big problem.
These are exceptional, and incredibly expensive one-offs. Saying we can live on the Moon or Mars based off of that is like saying most humans can be Olympic runners because someone did a sub-2 hour marathon, one time.
> but as far as I know there's no technical reason they can't
We can't even keep a dozen people alive in the Biodome, and if they didn't open it chances are the ecology would have collapsed or they would have run out of O2 due to the concrete messing with the CO2 & O2 ratios. And when something went wrong they just walked out -- and that ain't happening on the Moon or Mars. At least on the Moon you're a "short" flight away -- not months of solid burn away.
The point is 8b people live on earth! You can't build that many biosomes.
Edit: I forgot about radiation, silly me. I also enjoy having that blocked by earth’s atmosphere and magnetic field, again, some people might actually enjoy that and find that to be a business opportunity or whatever.