Stop thinking about outer space when we are in the middle of an anthropogenic mass extinction here on planet Earth.
Well, we don't know that it's the most habitable; it's just the most habitable we know of. And huge sections of it are completely unsuited for human life. 2/3rds of it will kill a human being in a matter of hours. Anything above or below, let's call it 50 degrees latitude is inhospitable without technology, and the equator isn't a great place to live, either.
OTOH I disagree with the notion that we have to have a full grasp on how to sustain us on this planet before we can make other planets inhabitable for us. I think there are things we will only learn if we try. I am not saying that trying right now is feasible, though.
Invasive species don't co-evolve to exploit the ecosystems they stumble upon. They happen upon a ecological space where there are incredibly low hanging fruit that they are better equipped at taking advantage of. Imagine space-faring humans stumbling upon a world where the oceans resemble that of the Earth's as they once existed in the 1500's--a world densely populated with an abundance of marine life, ripe for harvesting.
While there is some probability that biochemistry is not 100% universal (ie. alien metabolites could be toxic to humans or cause an immune response), I imagine there are scenarios where the same set of molecules and polymers are used. The principles of biochemistry are going to be similar in a lot of places in terms of how energy is exploited and harnessed.
I think it's incredibly more likely that humans will never be interstellar travelers en masse than to say that Earth is the optimal naturally occurring human habitat in the universe. As far as we know there is an infinite space full of limitless planets. Plenty of biological solution space with which to theoretically work / exploit.
In that case I think you should dial it back a bit. Humans are pretty adaptable. Even assuming the changes in temperature and sea-level are on the high end of predictions, we will adapt. People will move, infrastructure will be built, and so on. Mass extinction certainly isn't going to happen from global warming as we understand it today.
You might argue there there will be mass casualties, but that is also uncertain, difficult to quantify, and is quite a different thing than 'mass extinctions'. Of course, mass casualties due to weather has and is already a problem -- it isn't something that is uniquely associated with global warming.
I assume the parent is referring to the https://en.wikipedia.org/wiki/Holocene_extinction which is certainly happening, and has been for thousands of years.
Climate change is a rather recent contributor, albeit a very serious one of which we've only glimpsed the beginning.