How did Matthew Arnold, in the light of the nineteenth century discoveries in science and the Higher Criticism, read the Bible?
Answer: As literature and poetry.
This from the excellent 1967 The Encyclopedia of Philosophy (Volume 1, 168):
[I]n Literature and Dogma (London, 1873) Arnold offered to “reassure those who feel attachment to Christianity, to the Bible, but who recognize the growing discredit befalling miracles and the supernatural.” For any adequate reading of the Bible, after the effects of the Higher Criticism and the scientific controversies, the spirit of culture was indispensible. Only by this approach could the Christian ethic, and its intense expression in the Scriptures as read undogmatically, be preserved in a time of inevitable change. In particular, it was necessary to understand that “the language of the Bible is fluid, passing and literary, not rigid, fixed, and scientific”; its truth had to be versified through reading, rather than merely assumed. The Christian ethic so verified would be stronger than the dogmatic theology that had made the Bible into what it evidently was not.
Matthew Arnold also said of the Bible, “The personages of the Christian heaven and their conversations are no more matter of fact than the personages of the Greek Olympus and their conversations” (God and the Bible, 1875).
And here’s Punch, in 1881, caricaturing Arnold:
Source for both images: Wikipedia