We have already had some questions on this topic, but mine concerns the philosophy espoused by non-canon sources. I am interested in any specific example of why early Christian leaders may have thought an excluded text was incompatible with the 'message' of the New Testament (whatever that is), so please don't feel constrained by the title.
Let me answer your question in two parts. Yes, the NT Apocrypha certainly contains all sorts of things that are difficult to mesh with the canonical NT. For example, in the (probably) 2nd century Infancy Gospel of Thomas, we read the following:
3 1 While he was going from there with his father Joseph, a child running tore into his shoulder. And Jesus said to him, “You shall no longer go our way.” And instantly he died. At once the people, seeing that he was dead, cried out and said, “Where was this boy born that his word becomes a deed?” 2 When they saw what had happened the parents of the dead boy blamed his father Joseph, saying, “Because you have this boy you cannot live with us in this village. If you wish to be here, teach him to bless and not to curse.” (This is Tony Burke's translation from here.)
Jesus, according to this text, spends an inordinate amount of his childhood being surly and striking people down like an out-of-control Anakin. Hardly the peace-loving Jesus of the Sermon on the Mount.
The more famous Gospel of Thomas (the Gnostic sayings one), contains all sorts of sayings-statements, some of which are fairly far from the collective mainstream of the canonical portrait of Jesus, others which are very similar. For example, 31:1-2, Jesus says, 'No prophet is accepted in his village. A physician does not heal those who know him.' is very close to cf. Mt 13:57 and perhaps Mt 9:12. But this is the same Gospel that suggests that Mary and women need to become male to enter the kingdom of heaven (114:1-3).
Other apocryphal texts likewise portray the emergence of later theology very clearly. The 2nd century Acts of Paul includes a text, Acts of Thecla, with a very heavy emphasis on virginity as well as promoting the independence and autonomy of female teachers, the former of which appears early but not first-century early, and the latter of which is not-mainstream at all for hte early church (except the Montanists perhaps).
So, yes, the Apocrypha are full of things that are divergent from the canonical texts. But on to part 2, and that is dealing with a misconception about how texts were canonised. It's very unlikely that a community or even leaders sat down at any stage with, say, 15 gospel texts and said, "Okay, which ones are in and which ones are out". Text usage and selection happened much more organically, and there are significant differences between most of the Apocrypha and the canonical texts. Firstly, apocryphal texts generally emerge later (the majority are second century), are tied more directly to non-mainstream groups and their theologies reflect that. They would have been in use among those non-mainstream groups, either as replacements or supplements to what we think of as the New Testament. For the most part, texts now classified as apocrypha never really won widespread acceptance. They weren't 'rejected', they were never 'accepted'.
Another element of this is that most of the Apocrypha are qualitatively different. Many of the texts currently called 'Gospels', i.e. of Peter, James, Thomas, Eve, etc., are not really gospel texts - they are not biographical narratives dealing with the life and death of Jesus at all. The two texts I references above, Gospel of Thomas and Infancy Gospel of Thomas, are a sayings collection and an Infancy narrative, respectively.
The best place for this question is going to be /r/academicbiblical.
Here is a link to their wiki page on the history of the bible, including a section on apocrypha. I would start there and then repose your question in their sub if you didn't find an answer in the FAQ.