Historically, the canon is primarily those books that a given church uses in worship. It hasn't normally been a formal decision, but what became customary. E.g. because the church after the first few decades were primarily Gentile, they used the standard Greek Old Testament. It included the Deuterocanonical books. Not all copies were the same, so various eastern Orthodox communities have slightly different sets of books. I don't get the impression that the OT canon was ever seen as a big issue in the early days.
It became controversial during the Reformation. The Reformers wanted to move back closer to the Apostles. As part of that they started using the OT in Hebrew. But the Hebrew canon is smaller than the Greek canon. Jews had a different attitude towards the canon than modern Protestants: they had different levels of attention, with the Torah being the heart, followed by the prophets and the "writings." The later books never made it into Hebrew, but became part of the Greek OT, but wouldn't have been regarded as at the same level as the Torah.
Protestants, however, with sola scriptura, began to see all of Scripture as authoritative. As this developed over the next generation or two of Protestants, the canon became very critical. If you could take any verse of the BIble and use it to establish doctrine, it matters very much what is in the Bible.
I believe the absence of the D-C books started out as a consequence of moving to the Hebrew OT. But since key texts for a few Catholic doctrines were present in the D-C books, it turned into an ideological issue. For that reason, around the Reformation there was authoritative decisions about the canon. On the Catholic side this was done at Trent. On the Protestant side, many of the confessions list the books. Interestingly, the early Lutheran tradition left the canon open. Lutheran confessions don't include a specific list, and until fairly recently Lutherans were free to disagree. As conservative Christianity has coalesced around Evangelical theology, conservative Lutherans have de facto mandated the usual Protestant canon.
Mainline Protestants have an attitude closer to the original Jewish one. We look at each book critically. We don't make doctrine from individual passages, but look how concepts are used throughout Scripture. In the process we may see that different authors take different views. We tend to prioritize, giving the Gospels first priority and then Paul. We use the OT only with care. So a few books more or less aren't big deal to us, if they aren't key books (e.g. the Gospels, the undisputed letters of Paul, the major prophets).