You can strongly see the cultural influence of Islam in Turkiye, North African and Pakistan.
Also in the US blue looks correlated with larger latinx populations, matching the much bluer populations in central and South america.
It also looks like more extreme climate weakly selects for more gender segregation - look at the more barren southern parts of South America, far north Canada, Scandinavia - but the effect of culture is clearly stronger.
You can see the Muslim populations in other parts of Europe: Albanians in Albania, Kosovo and Western half of North Macedonia. In Bosnia the Bosnian parts are more red as well, Northern and Eastern Serbian parts are lighter:
Serbs are Orthodox Christians, Bosniaks are Muslim and the minority Croatians are Roman Catholics historically.
What is the reason for the big divide in Brazil and Argentina? The blue parts have more indigenous descents, while yellow is predominantly European?
I think that it's less about direct descendants and more about cultural influence. For example, contrast the map in the OP with this one:
Sure, it kind of fits for the Northwest, but not for Patagonia - that has a rather large indigenous population and yet it's tan-coloured. Look also at Misiones: pretty much the opposite happens, it's blue in the map but your typical person there is an European descendant.
Same deal with Brazil, although African heritage is likely more typical than Amerindian heritage.
I wonder how the source is biased. Like, what demographic in what country is on Facebook, in how far people befriend others more or less easily online vs offline, how do such female vs male "networks" come together. Do they clarify this in the article?
There must be another factor to this as well since the split is mostly the topmost countries some of the majority Islamic countries in this map are blue in the other map
Interesting Maps. In OP's PDF Link is also a map of the middle east (it is as you expected it).
The weird one I found was South Korea. It is a Democracy and pretty modern, but still pretty low values.