While climate changes have always existed, there are now at least 2 important differences, which will make this warming much more dangerous for the terrestrial plants and non-human animals.
One difference is that the rate of warming is very high now, probably much higher than ever before. At least where I live, in Europe, the climate has changed dramatically in less than 1 human lifetime and now it is extremely different from how it was when I was young.
The second difference is that now all larger wild animals and wild plants will no longer be able to react to climate like they did before, when they migrated towards the south or towards the north, depending on the climate evolution.
Now the terrestrial part of the Earth is mostly occupied by humans, crops and domestic animals, while the remaining wild plants and animals are mainly in "islands" scattered over the lands. This will make impossible a gradual retreat of the wildlife towards some more appropriate climate and they cannot make plans like humans, e.g. that they should travel 100 km through some inhospitable land, because at the end there would be a suitable biotope.
Of course, among the terrestrial wildlife, the best chances for surviving a climate change will be for those who can reach far distances through the air, over the man-made obstacles, e.g. plants with airborne seeds, birds, bats, insects, spiders and other very small living beings that can be carried by the wind, or by birds or insects.
In any case, it is pretty certain that this warming will be much more destructive for the wildlife than any other before.
whose conclusions are that, by mass, the humans alone are many times more than all the wild terrestrial vertebrates together, while obviously the domesticated animals exceed a few times the humans, both in number and mass.
Of course the number and mass of animals are only partially correlated with the area occupied by them, because the larger some wild animals are, the less their surface density is, and except for animals as small as rodents or small birds their surface density is much less than that of humans in cities.
There are a few countries with a relatively low density of population, e.g. most of North America, Russia, Australia, the northern European countries (Finland, Sweden, Norway).
I am not familiar with the land status in these countries, but these are the only places on Earth where there is a chance for some areas occupied by wildlife to form a connected mesh, allowing slow migration, but even that must be sectioned by many roads and fences that may discourage the migration of animals from the places that they have inhabited from birth.
Other low human density areas on Earth, i.e. the tropical forests and the deserts, do not count, as they will not be destinations for animals or plants seeking lower temperatures. Of the other areas with low human density, only in the high mountains there would be possible migrations, when the animals and plants adapted to high altitudes and lower temperatures could die and be replaced by animals and plants coming from lower altitudes. Except that in many countries most of the wildlife is already in the mountains, so there might be very few wild animals and plants left at lower altitude, ready to replace the former inhabitants from high altitudes, which will never have any way out.
On the other hand I am more familiar with the status in Western and Eastern Europe and in some parts of Asia, where I have traveled frequently through several countries.
Here, it is enough to fly a plane over several European countries in a sunny day, and you will see only agricultural land, villages and cities, with only isolated and scattered remains of forests, lakes or uncultured land, or isolated parts of mountains that remain wild.
There already is a great difference between how some places were when I was young and I traveled to them and how they are now. Several decades ago, there were relatively large connected wild areas in some mountains, but meanwhile a lot of roads have fragmented the mountains, owners have built fences around land parcels, some forests have been cut and so on, so where there was a larger wild area now there are many disconnected smaller wild areas.
That doesn't mean conditions will be to our liking under those regimes. We built cities along coasts assuming a certain mean sea level. We built farms assuming certain weather patterns.
If we cause large changes to these patterns in a relatively short period of time that's bad. The long-term trends you are talking about happened very slowly - slowly enough in theory a city could move back from the shoreline without anyone noticing it was happening. Slowly enough that species can migrate or adapt to them - slow enough natural selection can produce individuals more heat or cold adapted.
Climate change isn't going to cause humans to go extinct or anything like that. But it is going to have large and sometimes unpredictable effects, most of which are not useful or helpful to us. Many of which are actively detrimental.
Since the oil/coal/natgas will eventually run out anyway and the world so depends on them that gives leverage to people who really really want to hurt us: we might as well just deal with it and move away from burning things as much as possible.
> There were millions of years without ice caps even
In case anyone was curious, this is a significant understatement. It is currently believed that the Earth had no ice caps for its first 2 billion years, before the Huronian glaciation, and then again no ice caps for another ~1.5 billion years.
Why bother? There weren't humans millions of years ago to record climate data or grape picking dates. Writing is 5500 years old. Climate change could have ended the Roman Empire. In wide terms we already know what will happen because it happened before.
At the end of a glacial period the temperature changes rapidly e.g. it took 100 years for the land ice to retreat from the Eifel range in Germany (at 50°N) to above Oslo in Norway (at 62°N), a distance of 1200 km at the end of the younger Dryas some 12.000 years ago:
The planet has been +- 10 degrees from here. There were millions of years without ice caps even