Searching for a short story about the crucifixion

The only story I know that involves time travel and the crucifixion is Michael Moorcock's Behold the Man, originally released as a novella in 1966 and later expanded into a novel in 1969. Wikipedia describes it as:

an existentialist tale about Karl Glogauer, a man who travels from the year 1970 in a time machine to 28 AD, where he hopes to meet the historical Jesus of Nazareth.

Things, naturally, take a turn for the worst.

However, this doesn't explicitly match the description you've given. It's not about why there are no time travelers to Jesus' time. However, since the description is vague, and also second-hand, I figured it might be the right one. I've glanced over Card's Maps in a Mirror collection, but couldn't find a story that matched your description.

Your description is a good match for Up the Line, a novel by Robert Silverberg. The Crucifixion flash crowd paradox was addressed directly but no one ever figured out why the expected hordes were not present.

Excerpt:

I spoke the other day of cumulative audience paradox. This is a severe philosophical problem which has not yet been resolved, and which I will present to you now purely as a theoretical exercise, to give you some insight into the complexities of our undertaking. Consider this: the first time-traveler to go up the line to view the Crucifixion of Jesus was the experimentalist Barney Navarre, in 2012. Over the succeeding two decades, another fifteen or twenty experimentalists made the same journey. Since the com­mencement of commercial excursions to Golgotha in 2041, approximately one tourist group a month—or 100 tourists a year—has viewed the scene. Thus about 1800 individuals of the twenty-first century, so far, have observed the Crucifixion. Now, then: each of these groups is leaving from a different month, but every one of them is converging on the same day! If tourists continue to go up the line at a rate of 100 a year to see the Crucifixion, the crowd at Golgotha will consist of at least 10,000 time-travelers by the middle of the twenty-second century, and --- assuming no increase in the permissible tourist trade --- by the early thirtieth century, some 100,000 time-travelers will have made the trip, all of them necessarily congregating simultaneously at the site of the Passion. Yet obviously no such crowds are present there now, only a few thousand Palestinians --- when I say "now" I mean of course the time of the Crucifixion relative to now-time 2059 --- and just as obviously those crowds will continue to grow in the centuries of now-time. Taken to its ultimate, the cumulative audience paradox yields us the picture of an audience of billions of time-travelers piled up in the past to witness the Crucifixion, filling all the Holy Land and spreading out into Turkey, into Arabia, even to India and Iran. Similarly for every other significant event in human history: as commercial time-travel progresses, it must inevitably smother every event in a horde of spectators, yet at the original occurrence of those events, no such hordes were present! How is this paradox to be resolved?

Miss Dalessandro had no suggestions. For once, she was stumped. So were the rest of us. So was Dajani. So are the finest minds of our era.

This is probably just one of many stories that match your description, but how about Time Prime by Geoffrey A. Landis? The point of the story is that time travel into the past is only possible once someone has built a receiver.

The story doesn't directly reference the crucifixion, but in the intro Landis says:

You'd think that, if it were possible to make a time machine, the past would be full of time travelers. Historic events like the crucifixion or the battle of Gettysburg ought to be full of time-traveling tourists. So where are they? But what if a time machine requires not just a transmitter, but also a receiver?

The short story 'Let's Go To Golgotha' by Garry Kilworth (first published in 1975) ends with the revelation that there's nobody at the Crucifixion except time-travelling tourists....

From Alfred Bester's "The Men Who Murdered Mohammed":

“My boy,” I said, “time is en­tirely sub­jec­tive. It’s a pri­vate mat­ter—a per­sonal ex­pe­ri­ence. There is no such thing as ob­jec­tive time, just as there is no such thing as ob­jec­tive love, or an ob­jec­tive soul.”

“Do you mean to say that time travel is im­pos­si­ble? But we’ve done it.”

“To be sure, and many oth­ers, for all I know. But we each travel into our own past, and no other per­son’s. There is no uni­ver­sal con­tin­uum, Henry. There are only bil­lions of in­di­vid­u­als, each with his own con­tin­uum; and one con­tin­uum can­not af­fect the other. We’re like mil­lions of strands of spaghetti in the same pot. No time trav­eler can ever meet an­other time trav­eler in the past or fu­ture. Each of us must travel up and down his own strand alone.”

Doesn't specifically address the Crucifixion, but it is an answer.

I can recall a short story printed at Easter in the Otago Daily Times, I think in the 1980s. This involved a time travel travel agency that organized time trips to significant events. This particular group were attired appropriately and transported to the trial scene of Christ where they joined with the crowd in demanding his crucifixion. After the event, as they were returning to assembly point for return, they noticed the general sadness of the inhabitants of the time who were clearly distressed, and, by implication, against the crucifixion. It then dawned on the more erudite of the travelers that it was the people from the future and not specifically the people of Jesus' time, who had been instrumental in crucifying him. An important theological truism. I have never been able to track the story down since then but would love to do so.

The short story "Ripples in the Dirac Sea" by Geoffrey A. Landis features a time traveler who tries to visit the Crucifixion but fails. The reason for his failure has less to do with the mechanics of time travel and more with his lack of preparation. He doesn't speak the language, isn't wearing the right clothes, and didn't "land" very close to the site where the crucifixion is taking place. Because of this, he runs into some bandits who rough him up and leave him for dead by the side of the road. He doesn't make a second attempt after that.

So there is nothing really preventing time travelers from attending the Crucifixion. But on the other hand, the story does explain why there is no historical record of these visitors (spoilers):

The crucifixion trip is just one small portion of the story, not the main emphasis. Here are the main points:

• Set in the "present day" of the time the story was published (late 1980s), or close enough to it to make no real difference.
• The main character is a man who is part of a scientific team that has just invented the time machine. They are about to announce their discovery at a big conference.
• The nature of the time machine is essentially "round-trip": anything or anyone that uses the machine to travel to the past must eventually return to the exact moment that they left.
• Right before the big conference,
• The main character spends most of the story hanging around with hippies in San Francisco during the Summer of Love (1967).
• The main character discovers that his team was mistaken about the nature of the time machine they built: