Capitalizing "Biblical" when it's used as an adjective pointing to God's Word is acceptable, stylistically; but more, it's a confession of faith. So why is the Chicago Manual of Style (CMOS) agin it?
In few areas is an author more tempted to overcapitalize or an editor more loath to urge a lowercase style than in religion. That this is probably due to unanalyzed acceptance of the pious customs of an earlier age, to an unconscious feeling about words as in themselves numinous, or to fear of offending religious persons is suggested by the fact that overcapitalization is seldom seen in texts on the religions of antiquity or more recent localized, relatively unsophisticated religions. Is is in the contexts of Christianity, Judaism, Islam, Buddhism, and Hinduism that we go too far. The editors of the University of Chicago Press urge a spare, down style in this field as in others: capitalize what are clearly proper nouns and adjectives, and lowercase everything else except to avoid ambiguity. (CMOS, 14th ed.)
The above is a good summary statement of the significance of orthodox and pious Christians continuing to capitalize "Biblical" when it refers to Holy Scripture... In their online forum, CMOS is asked why, concerning "biblical," they depart from their general rule concerning the capitalization of proper adjectives (as opposed to common adjectives)? After stating their preference once again, they cede the legitimacy of "Biblical" with this final sentence:
If you must capitalize “biblical,” however, you have our blessing (as long as you do so in a consistent and logical manner).
We must, and we're grateful for your blessing.
For a couple helpful discussions of this question, see