The stress laid by traditional Christianity on getting right what may seem to be abstruse aspects of the doctrine of the Trinity is, I expect, puzzling to non-Christians and even some Christians. But there is a simple consideration here. The Christian is already here and now caught up into the eternal life of the Trinity (this claim may depend on Catholic and Orthodox views of sanctification), worshiping the Father through the Son in the Holy Spirit.
Crucified together with Christ (Christô sunestauromai), it is no longer I who live, but Christ lives in me, and the life I live in flesh I live in faith in the Son of God, who loved me and gave himself for me. (Gal. 2:20).
But participation in the life of the Trinity should integrate the whole person, which is why the most common traditional prayer of the Christian is not just in words, but in body—it is the Sign of the Cross where we proclaim our co-crucifixion with Christ with our hands and our faith in the Trinity with our words. A part of this integration is the life of the intellect. When the Gospels report Christ's giving us his version of the Shema`, the Shema` is amplified. Whereas the Old Testament exhorted us love God with "all your levav, all your being (nefesh), and all your might" (Deut. 6:5), in Mark 12:30 the levav—which is traditionally translated "heart" in English though it equally includes the mind—is expanded into both "heart" (kardia) and "mind" (dianoia). There is something right about the Jewish focus on intellectual life, the life of study, as essential to religious practice.
To participate in the life of the Trinity with the whole person also involves an intellectual participation, insofar as one is capable of it. After all, the second person of the Trinity, who lives in us, is the divine Wisdom, the divine Logos—an intellectual participation is, thus, an essential part. Faith involves both an act of the will and an act of the intellect. In meditating on the doctrine of the Trinity, as revealed in the Scriptures and as embodied in the life of the Church, we participate in an imperfect way in the life of the Trinity, where the Logos is the Father's knowledge of himself, as Sts. Augustine and Thomas say. We already participate in the heavenly life, and that heavenly life includes intellectual participation in the life of the Trinity.
Doctrine, thus, matters. Insofar as we get it wrong, we do not participate in the heavenly life. Of course innocent mistakes will be rectified when we attain the fullness of heavenly life. But love for God should impel us now to know that triune God whom we love, for love seeks knowledge and knowledge propels love further.
[Edited: Changed description of triune aspects of worship to match traditional formulation.]