- this constructs the other as gentile/infidel/heretic
2. Understanding the gods of the others as (our) demons

    - this produces the image of the  other as a 'Satan lover' or demon-worshiper - this aspect is especially strong in Christianity. 

I am now reading in between my other readings, purely for pleasure, the Histories of Herodotus (yes I'm weird - I actually enjoy reading them) and I was struck about his presentation of the religion of the Egyptians which contains a very different approach.

The Greeks tell many tales without due investigation, and among them the following silly fable respecting Hercules:- "Hercules," they say, "went once to Egypt, and there the inhabitants took him, and putting achaplet on his head, led him out in solemn procession, intending to offer him a sacrifice to Jupiter. For a while he submitted quietly; but when they led him up to the altar and began the ceremonies, he put forth his strength and slew them all." Now to me it seems that such a story proves the Greeks to be utterly ignorant of the character and customs of the people. The Egyptians do not think it allowable even to sacrifice cattle, excepting sheep, and the male kine and calves, provided they be pure, and also geese. How, then, can it be believed that they would sacrifice men? And again, how would it have been possible for Hercules alone, and, as they confess, a mere mortal, to destroy so many thousands? In saying thus much concerning these matters, may I incur no displeasure either of god or hero!
(...)
I therefore maintain that Melampus, who was a wise man, and had acquired the art of divination, having become acquainted with the worship of Bacchus through knowledge derived from Egypt, introduced it into Greece, with a few slight changes, at the same time that he brought in various other practices. For I can by no means allow that it is by mere coincidence that the Bacchic ceremonies in Greece are so nearly the same as the Egyptian- they would then have been more Greek in their character, and less recent in their origin. Much less can I admit that the Egyptians borrowed these customs, or any other, from the Greeks. My belief is that Melampus got his knowledge of them from Cadmus the Tyrian, and the followers whom he brought from Phoenicia into the country which is now called Boeotia. 
Almost all the names of the gods came into Greece from Egypt. My inquiries prove that they were all derived from a foreign source, and my opinion is that Egypt furnished the greater number. For with the exception of Neptune and the Dioscuri, whom I mentioned above, and Juno, Vesta, Themis, the Graces, and the Nereids, the other gods have been known from time immemorial in Egypt. This I assert on the authority of the Egyptians themselves. The gods, with whose names they profess themselves unacquainted, the Greeks received, I believe, from the Pelasgi, except Neptune. Of him they got their knowledge from the Libyans, by whom he has been always honoured, and who were anciently the only people that had a god of the name. The Egyptians differ from the Greeks also in paying no divine honours to heroes.

Here is rundown of a couple of things I found interesting and surprising about this account:

- using the ritual logic of the other's religion to criticize your own religion's myth about the wrongness of the other's religion (cf. the Heracles episode)

- that religions have a history

- that similarities in ritual structure are not mere coincidences but are indicative of relationships between two religions

- that religions are transmitted by people being in contact with each other

- that names of deities can indicate their cultural/historical origin

Beyond all this, I think that by far the most interesting thing is that this relativistic and historicist attitude does not lead to a pessimistic conclusion about the validity of religion.

In modernity historicism has been deployed to show that because religions have a history of transmission they are just human activities, creating a kind of 'nothing godly to see here folks, just humans doing their thing' attitude. 

Herodotus does not share this intuition at all and because of this he is no modern avant la lettre. For him, showing that Greek religion is historically related to the Egyptian actually augments its validity and truth. It serves as a confirmation in the sense of 'look they believe it too so it must be true.' In Herodotus' sense, showing that a religion is isolated and unique would actually be a skeptical argument.