The seventy-two angels are a Christian system built from Jewish materials, and the seam is visible if you look for it.
The materials are unambiguously Jewish: a Hebrew consonantal text, a counting procedure attested by Rashi, a development in the Bahir and the Zohar, and a body of speculation about divine names that runs through the whole of Kabbalah. Nothing about the derivation requires or suggests Christianity.
The system built on it is unambiguously Christian. Christian Kabbalah begins in the late fifteenth century with Pico della Mirandola, who argued that Kabbalistic method, properly applied, confirmed Christian doctrine. Reuchlin gave the movement its scholarship. Agrippa incorporated it into the Three Books of Occult Philosophy in 1533. From there it runs through the seventeenth-century compilers, the eighteenth-century French occultists, the nineteenth-century revival and the Golden Dawn, and into every modern presentation of the seventy-two.
The additions made along that route are Christian in structure. The nine choirs come from Pseudo-Dionysius. The verses attached to the names are taken from the Psalms as numbered in Christian Bibles. The pairing of each angel against a demon of the Goetia is a Christian demonological arrangement. The tarot is a European card game given an esoteric reading in eighteenth-century France.
This is not a criticism of either tradition. It is a statement of provenance, and it has a practical use: it tells a reader which sources are likely to be informative about which parts. For the derivation, the Jewish commentators. For the angelology, the Christian humanists. For the correspondences, the Victorian occultists. Asking any of them about the others' work produces confusion, and a great deal of the modern literature is confused in exactly that way.