The claim that you are “spiritual but not religious” has reached cliche status in American culture. But in the evangelical and Reformed tradition, there is really no possibility of being “spiritual” without being regenerate. The “spiritual” state to which the Bible refers is not a vague experience of being in touch with the universe, but the precise state of being made new by the Holy Spirit of God, the third person of the Trinity. Jonathan Edwards explained this distinction in Religious Affections, arguably his most important treatise.
Another reason why the saints and their virtues are called spiritual (which is the principal thing), is that the Spirit of God, dwelling as a vital principle in their souls, there produces those effects wherein he exerts and communicates himself in his own proper nature. Holiness is the nature of the Spirit of God, therefore he is called in Scripture the Holy Ghost. Holiness, which is as it were the beauty and sweetness of the divine nature, is as much the proper nature of the Holy Spirit, as heat is the nature of fire. . . . The Spirit of God so dwells in the hearts of the saints, that he there, as a seed or spring of life, exerts and communicates himself, in this his sweet and divine nature, making the soul a partaker of God’s beauty and Christ’s joy, so that the saint has truly fellowship with the Father, and with his Son Jesus Christ, in thus having the communion or participation of the Holy Ghost.
The grace which is in the hearts of the saints, is of the same nature with the divine holiness, as much as ’tis possible for that holiness to be, which is infinitely less in degree; as the brightness that is in a diamond which the sun shines upon, is of the same nature with the brightness of the sun, but only that it is as nothing to it in degree. Therefore Christ says, John 3:6, “That which is born of the Spirit is spirit”; i.e. the grace that is begotten in the hearts of the saints, is something of the same nature with that Spirit, and so is properly called a spiritual nature; after the same manner as that which is born of the flesh is flesh, or that which is born of corrupt nature is corrupt nature.
But the Spirit of God never influences the minds of natural men after this manner. Though he may influence them many ways, yet he never, in any of his influences, communicates himself to them in his own proper nature. . . . Thus, for instance, the Spirit of God moved upon the face of the waters, and there was nothing disagreeable to his nature in that action; but yet he did not at all communicate himself in that action, there was nothing of the proper nature of the Holy Spirit in that motion of the waters. And so he may act upon the minds of men many ways, and not communicate himself any more than when he acts on inanimate things.
In other words, the Holy Spirit is ever moving in the world, and even acted in creation. Thus, he may move in the lives of “natural” people too. But the Spirit never “communicates” himself, or dwells in a person’s heart, except in true, regenerate believers.