First of all, thanks to all of you for your hard, under-valuated and beautiful job.
And about my question: For example, how people coped when suddenly there was no more Jupiter (or Mithra) but Jesus? Or no more Ahura Mazda, but Allah? The new religion was always imposed by force? It was like a king goes "Now we do this!" and whoever didn't comply was killed? Do examples exist in history of easy, slow and pacific religion changes?
Sorry for the dumb question, and if this is not the correct place (or way) to ask, let me know and I will change it. Thank you very much!
I can shed no light on the specific transitions you mention. But, if you're interested, I think the spread of Buddhism through East Asia offers a fascinating look at syncretism in practice. Rather than try and displace local religions, those proselytizing on behalf of Buddhism often preached that the local religions were themselves manifestations of Buddhism by connecting elements of the local religion to Buddhism. Chinese folk religion, for instance, had a deity, the goddess of mercy. Incoming Buddhists identified this deity with with the Bodhisatva Avalokitesvara, which got translated into Chinese as Guanyin. China's Guanyin is clearly the Buddhist Avalokitesvara, but Guanyin is also revered in religious Daoism, and has peculiar Chinese origin stories that don't always line up with the Buddhist scriptures. See, in Mahayana Buddhism, the bodhisatvas are beings who have achieved enlightenment as a buddha, but choose to remain in the cycle of death and rebirth in order to help all other beings achieve enlightenment as well. Their enlightenment and control over their own incarnations allows them to functionally choose exactly when, where and in what form they appear and have powers, basically. So, it makes sense from a Mahayana perspective that the deities of the local religions could very well be Bodhisatvas, but that the locals don't really understand what they're dealing with. Guanyin's Chinese and daoist sides have roots likely older than Buddhism's introduction to China, but the older deity and Avalokitesvara were sort of incorporated into one religion crossing entity.
Similarly, in Japanese Shinto there are many small, local deities. Shinto believes that basically everything, down to every rock and tree, has a 'kami' which is translated as 'god' or 'spirit'. So every town might have its own shrine dedicated to the local gods that were said to be active in the area. Buddhists would occasionally associate these gods with deities of Buddhist origins or with bodhisatvas.
This is interesting to me because it isn't quite the same as one religion incorporating another. Partly this was done to make it more palatable for people accept a new religion without feeling like they had to abandon their own traditions, but, there's also almost a sense that everyone was sort of already 'Buddhist', they just didn't realize it.
In particular I would like to hear what it was like for the Scandinavians to switch from their Norse gods to Christianity so quickly given how opposed these ideologies and beliefs inherent in these two religions were.