Two of three synoptic Gospels present a peaceful homecoming scene. Luke presents a mob that should have been able to kill Jesus. In narrative terms, there are two key distinctions between these very different depictions. The first is which characters were involved. The second is which phase of 'story time' in each overall narrative does or doesn't align with the episode under discussion.
To sketch briefly the theory I've been developing recently: Narrative contingencies purport watershed moments. For instance, the Gospels represent the time period of Jesus' rise to popularity in Galilee as being in strict correlation to John the Baptists's imprisonment. Whether that correlation is judged to be plausibly historical (or precisely historical) or not, what the correlation does inarguably accomplish is creating a strict point of demarcation within narrative story time. In the narrative structure, Jesus is not popular in Galilee *before* Antipas arrests John, but Jesus begins to get popular in Galilee *after* Antipas arrests John.
One effect of such contingent narrative developments is to restrict compositional selectivity. Whether or not this watershed moment depicts historical events accurately is a separate question. From a narrative standpoint, once the writer has laid down a plot and demarcated the "narrative timeline" of particular developments, any deviation from the narrative causality - in which plot implies temporal sequence, either with or against the flow of narrative sequence - creates a crisis of continuity. Again, this is merely a brief sketch, but it may suffice to point out that readers notice continuity errors. If the writer wants to talk about John *after* the beheading, he must clearly mention "when" such an episode happened. Apart from such cases, episodes are generally constructed to ensure they "fit" within the current phase of a developing continuity.
Now, apply this basic idea to the disciples. Matthew, Mark, and Luke each depict an early phase in Galilee during which Jesus was gaining notoriety. Whatever we call this, the "early phase" I have in mind is defined (de facto) as being *after* John's imprisonment but *before* Jesus calls his disciples. Of course, in a historical study it would be critical to note how the fourth Gospel nuances this somewhat, giving Jesus even earlier occasions for brief activity in Galilee and his introduction to some of the men he would eventually call. But whether John's account can be reconciled with the synoptic narrative structure (or its potential reflection in chronological events) is not in issue at the moment.
The issue at the moment is that three Gospels each present a homecoming scene within Nazareth. The question at the moment is whether each of these Gospel presentations is consistent internally, according to the continuity and contingencies of its own narratively constructed story world. Have these Gospels each successfully narrated a homecoming scene that belongs appropriately at the particular phase of the narrative storyline into which each writer has placed it?
In Mark and Matthew, the homecoming scene falls during John's imprisonment and several episodes after the disciples have been called and begun following Jesus consistently. In Mark's Gospel, the disciples are explicitly mentioned as being present (6:1), although no such mention appears in Matthew's nearly identical version (13:54-58). As mentioned above, the most obvious difference between these and Luke's presentation is that nobody tries to kill Jesus in Mark or Matthew's homecoming scene. In narrative terms, the key distinctions are character and story time. Mark and Matthew feature their scene in alignment with continuity, which is during the phase of the storyline when Jesus is normally accompanied by his disciples. Again, Mark even states this explicitly. They have all come to Nazareth with him.
However, in Luke's version, the homecoming scene is the first particular episode narrated upon Jesus' return into Galilee. Two brief episodes later, Jesus meets and calls Peter, James, and John. From that moment on in Luke's narrative, the disciples are regular fixtures in most scenes. Prior to that moment, Luke has only narrated two episodes of ministry in Galilee, but there is no reason to suppose an extremely unprecedented "flash forward" at Nazareth was the Gospel writer's secret intention. To the contrary, the nature of Jesus' homecoming scene in Luke's Gospel is such that inclusion *after* the disciples had been called would seem utterly problematic.
From a narrative standpoint, Luke cannot - without elaborate justification - selectively locate the homecoming mob scene within any phase of story time *after* the twelve have begun following Jesus. This point applies equally to the arresting scene in Gethsemane, where Luke goes through an elaborate explanation about Jesus' rebuking his followers' swordsmanship and then speaks to the chief priests before going away with them peacefully. If the soldiers came to arrest Jesus and his twelve 'blue collar' fishermen *didn't* make some kind of a protest, we'd rightfully take serious issue with Luke on that point. As it happens, Luke's homecoming mob scene is not encumbered by this same necessity of narrative explanation.
In short, Luke doesn't have to explain why the twelve don't interact with the Nazarene mob because Luke has located this scene in the phase of Galilean story time *before* Jesus had called his disciples to begin following him. There are two ways of looking at this narrative convenience. On the one hand, if Luke believed the mob action was an historical event, then its inclusion in the scene (de facto) has rather dictated to Luke precisely which phases of story time would or would not be appropriate for the temporal location of this scene, continuity-wise. If a mob really got to Jesus in Galilee, that kind of thing most plausibly would have occurred *before* Jesus called the disciples. On the other hand, if Luke has consciously invented the mob action ("from whole cloth" as it were) then the mob's inclusion likewise imposes the very same requirement as above. Fact or fiction, a narrative is representation of a plausible reality. Fact or fiction, when Luke determines to feature the mob seizing Jesus, Luke must place this episode in the phase of story time *before* Jesus' twelve (!) disciples begin following him everywhere. (How many Nazarene men, should the reader suppose, would have stood up against Jesus' whole entourage? And how many would it take to push past them and hold them back while dragging Jesus up towards a cliff?)
The story presented by Luke is entirely different than the story presented by Mark and Matthew.
Now, to answer the question at top: Did the disciples go with Jesus when he went to Nazareth?
Without appealing to historicity, the first answer is obviously that in Luke's story they did NOT go to Nazareth and yet in Mark or Matthew's story they did. Without appealing to historicity, that's the end of this inquiry. However, with considerations of historicity, this question's answer would depend upon whether one or both scenes might reflect one or more historical events. The old debates on this point were generally based in positivism, framing themselves as "Did Jesus visit Nazareth once or twice?" and so forth. As a matter of fact, that framing is actually as helpful as anything for illustrating why positivism ought to get buried forever. In the Gospel texts, we have possibly one or two accounts of Jesus' homecoming/s. But in real life - which does not necessarily align with OR automatically contradict the accounts of our texts - Jesus may have had zero homecomings, or three, or possibly more. As the fourth Gospel notes, "Jesus did and said many things..." so who's to say he did not have five, twelve, or seventeen ministerial homecomings? At any rate, whether historically or purely narrative-wise, the idea that each potential homecoming could have gone differently is entirely plausible, especially if you change the major practical conditions of each visit from one event to the next.
Finally, to return strictly and purely to narrative concerns, I will close with a related observation.
It is probably due to heavily entrenched positivism that scholars have long tended to speak about these two very differently narrated scenes as if they referred to one single homecoming event. From the standpoint of redaction criticism, even Darrell Bock discussed the literary issues as a matter of pure compositional selectivity, leaving tangible issues of situation and character strictly within the domain of historical concerns.
As should be apparent by now, I believe the category of narrative is more of a crossover that contains something of both the traditional literary world and the actual physical world. Narrative is not automatically history, but narrative is not merely linguistic, either. Narrative is the linguistic representation of a plausible story world that follows physical and historical rules. We can no longer subscribe to positivism that restricts the story world to being merely the precise words of a text. Aside from that not being how historical narrative works, that's not even how fictional narrative works.
From a narrative standpoint, we must conclude these two scenes depict two very different potential realities. We conclude this because of the narrative elements in each which are so completely divergent from one another. If Luke has "modified the content of Mark's text", he has also modified the characters involved, adjusted which phase of story time the episode belongs in, and introduced a major conflict that did not exist in the previous version. One could also argue for differing focalizations and themes, but character, setting and plot/conflict are the major elements in any story world so the argument as is should be easily granted.
Considering why Luke adapts much of the text of Marks' episode remains a valid exegetical concern, and perhaps primarily a philological concern. Considering why Luke would cut and paste so meticulously as few ancient authors before Tatian had ever attempted or would ever imagine attempting, that's a valid concern for textual criticism and historical reasoning. But considering aspects of grammar or textual conflation to be more important or equally important to these narrative concerns in which the entire character of a basic story - not an elaborate emplotment or slanted narrativization, mind you, but three of the most basic elements of any story: setting, characters, and plot/conflict - that seems invalid in the extreme.
Historical narrative does not always or automatically convey a fair, honest, or accurate representation of historical events. Discussing these things in narrative terms can sometimes be a step towards making historical judgments but such discussion of narrative as narrative also has great value in itself, as this post is attempting to illustrate.
If the Gospel writer is viewed primarily as a textual editor or as a theologically minded exegete, then the Gospel redaction process will be reconstructed with such concerns being supposedly primary in the mind of the Gospel writer himself. But if the Gospel writer is viewed primarily as a storyteller - as someone who employed textual conflation and theological nuance when it suited their ends, but someone whose main objective was to construct a plausible, inspiring, and realisitc account of things which he wanted people to believe Jesus had actually done - then narrative concerns may possibly and perhaps normally hold greater value for interpretation, as opposed to previous ways of examining these issues.
All in all, these points should leave critics and scholars without further justification for discussing the homecoming scenes of Luke and Matthew & Mark as if Luke's presentation is merely a doctored version of Mark's. Although much text was borrowed, the narrative structure and content is so drastically altered that the narrative questions must trump. At the very least, once these issues are recognized, no scholar who believes Luke has begun from Mark's text should ever speak in terms of Luke telling a different version of Mark's story. With character, plot/conflict and temporal setting being so completely different, the only remaining commonality, apart from a bit of narration and dialogue, is their physical location.
In other words, in proper narrative terms, these episodes do not present the same story at all.