I believe you're referring to the Medieval Warm Period. As far as I understand, that was not a globalized event and did not affect global average temperatures significantly, like we're seeing now. But, like I said, I'm not a climate scientist so feel free to provide more sources on that.
Mastodons and saber-toothed tigers, etc, died out over a long period during the last extinction event c. 10K years ago (Quaternary megafaunal extinction). Climate change played a part plus other factors like the arrival of humans in the Americas which led to the loss of a lot of megafauna, I believe.
Versus species extinction we're seeing now which is faster and accelerating due to more rapid global changes in climate (along with ecosystem loss from other human activity plus pollution, of course, which possibly you don't disagree with).
In any case, 10K years ago the human population was tiny compared to now and people were much more mobile. Now that we have huge cities and billions of people with lives and livelihoods to lose, it's more of a big deal and the stakes are much higher. We've already seen how much damage is being caused by flooding, storms, heatwaves and wildfires, etc, across the world and how ill-equipped we are even in the US, the richest country.
On a purely economic level this is hard to deal with even now so if it gets worse we're gonna have a lot of expensive cleanup to do. (Also one factor driving current waves of human migration, by the way, along with conflicts, many of which we were directly involved in. Which manifests as simply an "immigration" problem for us, but we need to look at the bigger picture of why so many people are on the move in the first place.)
At the very least, I think we should be preparing ourselves by building flood defences and better infrastructure, whether we accept anthropogenic climate change or not. Because, even if it turns out we're not responsible (to play devil's advocate), the climate does appear to be heating up (much faster than during previous periods, in geological terms), and we have a lot more to lose than we did thousands of years ago now that we have so many settled populations and are largely urban.
Bangladesh is one of the most populous and densely populated countries on earth, for example. If sea level rises cause it to get flooded, we may have a lot more immigrants to talk about. Not to mention the geopolitical consequences. Obviously it's a super complex debate so there are no easy answers. My 2c.
