Some maps do overlap very well but in that case it only looks interesting because we want to see a causation link where there is correlation.
So sorry for the harsh words but I actually find this upsetting.
Sure, you could probably pick arbitrary political boundaries from different times and create maps that show the opposite trend. However, I would be surprised if there weren't correlative or causal factors, given that historical people reproduced and, in the case of many agrarian peoples, didn't migrate. It's possible that our collective ignorance of history makes this appear to be a novel fact, when we shouldn't be too surprised.
I still found it really cool to see how much an impact geography and path dependence has on our current state. I may be over generous, but when they show maps like the Alabama one where an ancient sediment deposit is correlated with farm size, racial makeup, and election results I think they are giving an example of how there can be common causes tied to geographies over long periods of time.
You're completely correct that simply overlaying the Austrian Empire's borders on a map of Romania's election results does not prove a causal link. It is much more likely that there is an underlying common cause (geographic feature, ethnic makeup, etc.). Pointing out these correlations is fun to me, as I'm able to speculate on the possible common causes.
Think about the countless numbers of ways you could overlay any sort of historical map over some map representing any kind of relevant statistic. A smaller but still countless number of them will have strong correlations by pure chance alone. This is a simple fact of statistics.
The author here is filtering out exactly those that happen to have those kinds of correlations backed by some preconceived ideas the author has about how the causality is supposed to work and uses them to fuel his hypotheses, while ignoring the uncountable number of map overlays that don't show these correlations.
This is bog standard selection bias.
For people who would like to see a demonstration of the effect yolo69420 is pointing out, you can visit the website below [1]. It, among other things, shows how Nicholas Cage movies are correlated with swimming pool drownings.
I completely agree that the Twitter post does not prove there is a direct causal relationship between the maps they compare, nor even that there exists a common cause. I would contend that this is a very high standard to hold for interesting content on the internet. If you would like to hold to this standard, you will likely come to more robust and defensible conclusions than myself.
I find it fun to speculate on possible common causes. If I had any actual ability to change things based on my conclusions, I'd likely increase my burden of proof to a much higher level like you suggest.
(https://www.youtube.com/watch?v=6JwEYamjXpA&t=2461s)
Some of these maps are for time period not that distant from each other where the correlation is pretty straightforward, and those are probably telling at-least-partly-true narratives. For others, it's less clear. How many different modern and ancient maps are there which could conceivably have interesting (spurious) correlations?