Judaism got its root in 1st millennium BC; Islam originated in 7th century AD; Christianity took birth in the 1st century AD. Did doctrinal differences regarding the Trinity necessitate the creation of these entirely new religions, or were there any other reasons?
Modern-day Judaism, which is a different religion compared to Judaism before Christ, is based on the Talmud, which they consider a sacred text at least on the level of the Torah (the 1st 5 books of the Bible). Islam is essentially a heretical sect of Christianity founded by Muhammad, who assembled the Koran from corrupted texts of Christian Holy Scriptures.
Judaism and Islam do not believe Jesus is God; this is a heresy according to Christianity. In addition to this, Judaism and Islam adhere to further errors that show they are false religions:
Christian Perspective on the Errors of Modern-Day, Talmudic Judaism
The cardinal, saint, and Doctor of the Church, Robert Bellarmine, wrote, speaking about the holiness of the Church's doctrine (On the Marks of the Church ch. XI):
From the Jews that wrote after the coming of Christ, it is manifest from their books. For in the first place, in the doctrine of the Talmud, which is their written word, not God’s, innumerable errors are discovered. Rabbi Solomon, whom the Jews reckon to be the greatest, teaches in his commentary on Genesis on that verse: “This now is bone from my bones,” that Adam had sexual intercourse with all the beasts and wild animals, and he could not satisfy his lust until he at last embraced Eve. The same rabbi, in his commentary on Numbers, in that verse On the first day offering holocausts to the Lord, he selects “the holocaust of the Lord,” and says it is a precept to offer a holocaust on the day of a new moon for the sin of God, which he committed when he diminished the light of the moon. The same Rabbi Solomon tells such a fable in chapter 1 of Genesis, on that verse “Two great lights;” and the same in chapter 4 of Deuteronomy, in that: God created man,” he says Adam was so grown, that he could touch heaven with his head, while he was on earth. Similar things occur everywhere in the books of the Jews.
See also Rev. I. B. Pranaitis's The Talmud Unmasked: The Secret Rabbinical Teachings Concerning Christians.
Christian Perspective on Islam's Errors
Discussing why it is not foolishness to assent to the truths of faith, although they are above reason, St. Thomas Aquinas, Doctor of the Catholic Church and its greatest theologian, writes, comparing Christianity to Islam (Summa contra Gentiles I cap. 6):
 This wonderful conversion of the world to the Christian faith is the clearest witness of the signs given in the past; so that it is not necessary that they should be further repeated, since they appear most clearly in their effect. For it would be truly more wonderful than all signs if the world had been led by simple and humble men to believe such lofty truths, to accomplish such difficult actions, and to have such high hopes. Yet it is also a fact that, even in our own time, God does not cease to work miracles through His saints for the confirmation of the faith.
 On the other hand, those who founded sects committed to erroneous doctrines proceeded in a way that is opposite to this. The point is clear in the case of Muhammad. He seduced the people by promises of carnal pleasure to which the concupiscence of the flesh goads us. His teaching also contained precepts that were in conformity with his promises, and he gave free rein to carnal pleasure. In all this, as is not unexpected, he was obeyed by carnal men. As for proofs of the truth of his doctrine, he brought forward only such as could be grasped by the natural ability of anyone with a very modest wisdom. Indeed, the truths that he taught he mingled with many fables and with doctrines of the greatest falsity. He did not bring forth any signs produced in a supernatural way, which alone fittingly gives witness to divine inspiration; for a visible action that can be only divine reveals an invisibly inspired teacher of truth. On the contrary, Muhammad said that he was sent in the power of his arms—which are signs not lacking even to robbers and tyrants. What is more, no wise men, men trained in things divine and human, believed in him from the beginning, Those who believed in him were brutal men and desert wanderers, utterly ignorant of all divine teaching, through whose numbers Muhammad forced others to become his followers by the violence of his arms. Nor do divine pronouncements on the part of preceding prophets offer him any witness. On the contrary, he perverts almost all the testimonies of the Old and New Testaments by making them into fabrications of his own, as can be. seen by anyone who examines his law. It was, therefore, a shrewd decision on his part to forbid his followers to read the Old and New Testaments, lest these books convict him of falsity. It is thus clear that those who place any faith in his words believe foolishly.
St. Robert wrote (ibid.):
As to the Muslims, the same is clear from the Qur’an. For it teaches that all are saved by their laws, if they should keep them, be they Jews, Christians or Turks. It also teaches everywhere that the beatitude of the future life consists in food and drink, and a multitude of wives, while no mention is ever made in the whole Qur’an of the vision of spiritual actions, or the love of God. In chapter 43 it says that God and the angels pray for Muhammad. Similar very absurd things are everywhere read in the Qur’an.
So, while Judaism's and Islam's erroneous views on the Trinity are a serious problem, that is not the only falsehood in these sects.