Can you say "economic agnostic" like in the following sentence?
Strategy cannot be economic agnostic.
No; agnostic there is an adjective and must be modified by an adverb, so you must say "economically agnostic".
But when you employ agnostic as a noun, the adjectival modifier is correct.
Prof. Sartorius is an economic agnostic; his proposal does not depend on either a Keynesian or a supply-side interpretation.