"Is there evidence that people were actually required to return to their ancestral home for a census as told in the Bible with Joseph and Mary?" Yes, no, sort of. We should probably untangle this a bit, because there are varying degrees of accuracy here.

Disclaimer: This is just an idle interest of mine. Our Bible specialists can give you a better answer, so hopefully you'll get one here to weigh in.

• Was there a census? Yes. This much we can prove. 6 CE saw a census under Publius Sulpicius Quirinius, who was governor of Syria between 6 and 9 CE. This is a matter of historical record and not something seriously contested by any historians studying the period. Both that and Matthew/Luke's comment on Herod's being ruler at the time have been an enormous help in dating the period described by the gospels. Problem is, they're just as problematic as they are helpful, because Herod's rule in Judea and Quirinius' becoming governor of Syria don't overlap at all. We think Herod died in 4 BCE because he helpfully expired not long after a lunar eclipse that can be dated (the eclipse story comes to us by way of Josephus IIRC) and Quirinius became governor 10 years later. So there isn't a census that took place under the reign of Herod the Great and Quirinius because their time in office, as it were, didn't overlap.
• Were people required to travel for it? Probably not. On top of being a somewhat mutinous province at the time, Judea was an administrative mess after unpopular rule by one of Herod's sons. The Roman census was conducted both to count the population and also assess Judea's tax burden as a vassal state. Naturally this depended on the nature and quality of assets owned by Judean citizens. It would have made little sense, and also would have been an enormous economic disruption, to have required everyone to return to whichever town was the seat of their tribe. Moreover, Joseph per the gospels was not a Judean citizen at all and would not have been part of the census.
• So where did the gospels get the story? First, not all, or even most, of the gospels contain the census story; it appears only in Luke. Second, scholars are generally agreed that the "census" moving Joseph, Mary, and the impending birth of Jesus to Bethlehem (or just their existing presence there in Matthew) was in service to a very old prophecy in the Book of Micah concerning the rise of the messiah. The messiah, wrote Micah, would be born in Bethlehem. Here was the messiah, insofar as the writers behind Matthew and Luke were concerned, so naturally he must have born in Bethlehem. Matthew simply places Jesus' birth there without further comment on why the family was there; Luke explains it by way of the census. Mark and John do not address the issue at all.

"And if that isn't historically accurate, shouldn't members of the nascent religion have been able to easily see that?" Not necessarily; none of the gospels were written during Jesus' life, or (probably) even shortly afterwards. The earliest gospel (which historians generally agree is Mark) was probably written somewhere between 12-40 years after Jesus' death. We're all too aware of the frailty of human memory, particularly in an era before easy or widespread access to government or historical records. Additionally, the gospels may not have been (and probably weren't) written by people who knew Jesus or had even seen him, but rather by people who collected accounts of his life and created a narrative around them. Matthew and Luke were probably written using Mark as a source in addition to other writings, included the fabled "Q source," a collection of Jesus' sayings and parables that most scholars believe existed. (If a copy is ever discovered, expect history and religious studies departments worldwide to wet themselves in joy.)

And to complicate matters even further, we may not have the earliest edition of the gospels on our hands. All the gospels were subject to later editing and additions, so ... what got added? What got subtracted? Were any mistakes made along the way? The early Christians certainly had a lot of arguments over which accounts of Jesus' life were canonical and which weren't, and we certainly know from the differences among Old and New Testament manuscripts that scribes made a good few copying errors.

So it would not necessarily have been easy for early Christians to see historical discrepancies in the narrative, and in fairness to the writers themselves, their narratives were written years (and most likely decades) after Jesus' death.

Source: Cyrus Gordon, The Bible and the Ancient Near East and Delbert Burkett's An Introduction to the New Testament and the Origins of Christianity.