Is the telling of the visiting magi, mentioned in the Gospel of Matthew, a made up fictional story?

Why would Herod care about some random foreign priests?

Herod was a king under the rule of the Roman Empire, which practiced a policy of religious tolerance, which is why the people of Judea were allowed to continue worshipping God to begin with. In the story of the three magi and Jesus's birth, we're told that three Zoroastrian priests see a star in the sky, and visit Jesus in the cradle.

Presumably, they would have had to have been fairly close by I'm order to do this, given that people can typically only walk about 20-30 miles per day - they would have already been located within Judea when they saw the sign. It's entirely possible that they were priests who tended to shrines or temples visited by a population of local Persian expatriates.

As such, what reason would Herod have for trying to stop them from peacefully going about their religious duties?

There are lots of fictional stories that have accurate historical references and are logically coherent. The fictional character of Sherlock Holmes is an example. So, showing coherence in the narrative, in being logical or conveying accurate historical trivia, does not prove that it was actually meant as history.

Mythicists may argue that the story of the magi gradually developed from its basic form to include their description as being three kings with specific names, differing geographical origins and subsequent histories.

However the fact that later Christians felt free to elaborate on an earlier tradition does not prove that the early church viewed Matthew's original account of the magi as a fictional story.

Eusebius (270-340 A.D.) writes about the church's view of the Gospel of Matthew being a true (i.e. not fictional) rendition of the life and sayings of Jesus when he writes (emphasis added):

John, who the whole time had made use of unwritten preaching, finally resorted to writing for the following reason: When the three previously written (Gospels) had already been delivered to all and to him, they say that (he) accepted (them), testifying to their truth,... (Eusebiu H.E. III.24.5-15)

That being said, one can still address the various form critical critiques that argue historical inaccuracies are in the account that demands it be taken as a fictional story.

Is it likely that the distrustful Herod would allow the Magi to go their way without at least a spy to watch their movements?...

My answer is that I think that the Parthian magi would have likely have been accompanied by a well defended entourage. Those military leaders could have easily been insulted if they found out Herod was sending spies to closely watch their movements. Herod would not have wanted to provoke a war with Parthia during a time of peace.

If Herod sent spies they would have needed to keep from being discovered in such a small town as Bethlehem. So, their ability to tell Herod specific details would have been limited. An angel is recorded in Matthew's Gospel as telling Joseph to leave immediately, even in the middle of the night. That would indicate Herod did a few things about what was going on. But it would have been too little and too late for him to deal with it.

A scholarly article on the subject notes the view of John Calvin. The author writes:

Because of the adverb, Τότε, which does not always denote uninterrupted time but can occur when there is great distance between events, Calvin believes that Herod may have thought the situation over for a year and a half before ordering the massacre of children two years of age and under.

The next question runs as follows:

What was the evangelist's source of information on such hidden matters as Herod's secret council with the Magi and the angel's apparitions to them and to Joseph?

As a tax collector, Matthew would have been good at taking notes. One reliable source he could have interviewed would have been Mary the mother of Jesus. She would have heard stories from Joseph. Mary was with the disciples after the resurrection of Jesus. Also, what she said could have easily been part of an extended conversation in the faith community that included members of the Sanhedrin like Nicodemus and Joseph of Arimathea. They would have been aware of the animosity of Herod toward the Jewish leaders and how his asking the question about where the Messiah was born (Matthew 2:4) either showed Herod's ignorance (See John 7:42) or was a possible set up.

According to Hippolytus (170-235 A.D), Matthew wrote the Gospel in Hebrew and published it at Jerusalem, and died at Hierees, a town of Parthia (Hierees is near modern day Tehran in Iran). So, given this Parthian connection, Matthew might have actually come into contact with the magi's descendants and their stories while doing mission work in Persia.

The final question runs as follows:

…why does neither Flavius Josephus, nor Jesus himself, nor John, Mark, Peter, Paul or any other apostle, nor even Luke in his infancy narrative, allude to this fact?...

My answer is that the other writers did not want to stir up trouble with Rome. The Parthians were a serious threat to Rome. Mathew, likely wrote his Gospel account of the magi visiting when the political tension was not that high.

The town of Bethlehem was rather small in the those days, so the slaughter of little children was rather insignificant compared to Herod's other evil things that he did. See this interview by the historian Paul Maier. He also notes:

Given the high infant mortality rate, the small town of perhaps 1,000 or 2,000 could not have had more than 30 infants of both sexes.

My reply shows that the grounds (included in the question) to falsify the narrative fall short. However, my comments are limited in that they do not add any insights on how it can be verified as historically true. For further thoughts on that, see this stack exchange discussion here.

My comments do not specifically address the view of John Dominic Crossan who argues about the magi story, "in plain language, it’s a parable...”

Showing coherence in the narrative, in being logical or conveying accurate historical trivia, does not prove that it was actually meant as history. There are lots of fictional stories that have accurate historical references and are logically coherent. The fictional character of Sherlock Holmes is an example.

Determining if the narratives were meant to be taken historical or as a fictional midrash like narrative is a complex issue. 2 Peter 1:16 appears to indicate that the apostolic community did not view fictional story telling as their modus operandi.

For we did not follow cleverly concocted fables when we made known to you the power and return of our Lord Jesus Christ; no, we were eyewitnesses of his grandeur. (2 Peter 1:16)

To add to the other excellent answers, I add a prophetic angle. This visit is not an unheralded event, but was foreshadowed by Solomon:

6 What is that coming up from the wilderness
like columns of smoke,
perfumed with myrrh and frankincense,
with all the fragrant powders of a merchant?
7 Behold, it is the litter of Solomon!
Around it are sixty mighty men,
some of the mighty men of Israel,
8 all of them wearing swords
and expert in war,
each with his sword at his thigh,
against terror by night.
9 King Solomon made himself a carriage
from the wood of Lebanon.
10 He made its posts of silver,
its back of gold, its seat of purple;
its interior was inlaid with love
by the daughters of Jerusalem.
11 Go out, O daughters of Zion,
and look upon King Solomon,
with the crown with which his mother crowned him
on the day of his wedding,
on the day of the gladness of his heart. 
(Song of Songs 3:6-11 ESV)

Observe that verses 6 and 10 list gold, frankincense and myrrh, the three gifts brought by the Magi. The Bridegroom is approaching the site of the wedding. Jesus referred to himself as the bridegroom. This passage also mentions Jerusalem and the crowning of a king by his mother.

The column of smoke in the desert brings to mind the pillar of smoke that guided the people of Israel through the desert of Sinai. It also is a fit description of the Magi's caravan, since their travels likely took them through the desert.

Also note that Solomon is accompanied by sixty soldiers bearing swords to defend against terror by night. What terror of night was worse that that which befell Rachel's children? Yet Jesus was protected from the terror stalking him.

Many other messianic parallels between the Song of Songs and the life of Jesus exist, but these should suffice.

Did the scribes and Pharisees know of these connections? If they spotted any of them, it would surely disturb them.

It is a common misconception that the wise men, or magi, visited Jesus at the stable on the night of His birth. In fact, the magi came much later. That is why Matthew 2:11 says they visited and worshiped Jesus in a house, not at the stable.

They came from "the East," most likely Persia, or modern-day Iran, a journey of almost 1,000 miles. It is probable that they knew of the writings of the prophet Daniel, who in time past had been the chief of the court seers in Persia. Daniel 9:24-27 includes a prophecy which gives a timeline for the birth of the Messiah. Also, the magi may have been aware of the prophecy of Balaam (who was from the town of Pethor on the Euphrates River near Persia) in Numbers 24:17. Balaam’s prophecy specifically mentions a “star coming out of Jacob.” Another Messianic prophecy specifies where the king was to be born:

And you, O Bethlehem of Ephrath, least among the clans of Judah, from you shall come forth to rule Israel for Me – one whose origin is from old, from ancient times” (Micah 5:1 - The Jewish Study Bible).

The magi, and their entourage, were guided to look for the King of the Jews by a miraculous stellar event, the “Star of Bethlehem,” which they called “His star” (Matthew 2:2). Here are a few extracts from an article that explores the background to the magi:

The word “magi” (singular: “magus”) originated centuries before the time of Christ to describe a caste of very learned priests and scholars among the ancient Medes and Persians... They were educated in the literature and languages of surrounding nations and in the equivalent of a world religions curriculum that included studies in divination, esoteric wisdom, magical practices, dream interpretation, and the zodiac (astronomy and astrology for them a single discipline).

... upon seeing the mysterious star in the East, they referenced it to Balaam’s prophecy in the Book of Numbers about the coming Messiah, which was prophesied hundreds of years before Christ’s birth: “I see him, but not now; I behold him, but not near. A star will come out of Jacob; a scepter will rise out of Israel” (24:17). This verse was usually treated as one of Israel’s messianic prophecies about the divine Ruler to come. Taking their cue from Scripture, the magi head for Jerusalem, the heart of Israel’s religious life, to seek further instruction. Source: https://wagingwisdom.com/2018/12/21/re-enchanting-the-star-of-bethlehem/

There is only one question I intend to address: What was the evangelist's source of information on such hidden matters as Herod's secret council with the Magi and the angel's apparitions to them and to Joseph? To answer that question here are some partial quotes about the author of this gospel:

The style of the book is exactly what would be expected of a man who was once a tax collector. Matthew has a keen interest in accounting (18:23-24; 25:14-15). The Gospel of Matthew is very orderly and concise. Rather than write in chronological order, Matthew arranges this Gospel through six discussions.

As a tax collector, Matthew possessed a skill that makes his writing all the more exciting for Christians. Tax collectors were expected to be able to write in a form of shorthand, which essentially meant that Matthew could record a person’s words as they spoke, word for word. This ability means that the words of Matthew are not only inspired by the Holy Spirit, but should represent an actual transcript of some of Christ’s sermons. For example, the Sermon on the Mount, as recorded in chapters 5-7, is almost certainly a perfect recording of that great message.

Matthew’s intended audience was his fellow Jews, many of whom—especially the Pharisees and Sadducees—stubbornly refused to accept Jesus as their Messiah. In spite of centuries of reading and studying the Old Testament, their eyes were blinded to the truth of who Jesus was. Jesus rebuked them for their hard hearts and their refusal to recognize the One they had supposedly been waiting for (John 5:38-40). Source: https://www.gotquestions.org/Gospel-of-Matthew.html

Within that article is the answer to your question, but you may have missed it. The accounts Matthew wrote about were inspired by Holy Spirit – they were “God breathed”. The story of the magi is no piece of fiction invented by Matthew, the tax collector who knew Jesus personally.