One way to interpret (alleged) topic neutrality in logic is to think of pure logic sentences/propositions as schematic sentences. Depending on the degree of schematism to a pure sentence's name, one might suppose that its (the sentence's) evaluation as true or false (or whatever) is unavailable unless the schematics are interpreted in such a way that they can be true or false (or whatever).
For example, one might represent a noncontradiction axiom as:
∀A∀~A: ~(A & ~A) (something like "for any pair of incompatible A, it is not (true) that A and ~A").
But you might be of a mind to be wondering whether we ought to impose this ∀-scheme on possible inconsistency unless we "checked" every pair of possibly inconsistent sentences (or facts, or whatever) to see whether the universal rule really holds. A strongly a priori (or, more clearly-put, a more proactive) model of "knowledge of logic" would allow that we can know the universal scheme to be true, indeed by knowing that all its instances (satisfactions) are true, but this because we sort of "project" all possible cases of the question (the question behind the schematics) into our reflective intellect and so we can then "see" how all possible cases are resolved/resolvable in advance. (When logical necessity and identity are tight-knit enough to questions of possible consistency, the immediacy of this "seeing" is acute to an ultimate extent, for then the identity of mere possibility in itself is made to turn on consistency as such.)
Or maybe logic isn't so topic-neutral after all, but is about things that are particular in their own way (or even nominalism is true, and everything is particular by the by anyway, but to mention that further would be to digress...). "No self-contradictory conjunction is true," or even, "Necessarily, no self-contradictory conjunction is true," might be an "instantly (ideally!) recognizable" logical fact. Or, "Every proposition is true or false," or, "There are Continuum-many truth-values,", or, "Truth is first and foremost an object named by true sentences, not as much a direct property of those sentences by themselves,", or, "The proposition, 'A,' is true if and only if A," or so on and on: some or all or none of these, and/or plenty of others besides, would themselves be true, or false, or both, or neither, or "only" one or the other, or "categorically false (resp. true)", even.
Now, if you're familiar with Lewis Carroll's musings on modus ponens, you might notice in the back of your thoughts a representation of logical rules not as assertions about metaphysical architecture so much as imperatives of inference and reasoning (or thought). John Stuart Mill, IIRC, traced the standard noncontradiction axiom to (I assume, based on his description) a "mental sensation" that we now often refer to as "cognitive dissonance." At any rate, one can construe the consistency requirement less as a matter of the truth-content of a belief and more a matter of the formal grounding of the belief. This is an especially perspicuous option if self-conflicting conjunctions "literally" turn into voids in our thoughts, i.e. if they are (sufficiently) "meaningless."
So, even so, for logical axioms that are elementary imperatives of understanding more than (or instead of) assertions or assertion schemes about abstract possibilities, we are at least referring to seemingly hypothetical imperatives, or moments in general instrumental reasoning: "If your end is inferring further truths from given truths, then..." Alas, the philosophy-pirates have smuggled truth-aptitude back into the capital city of the land of logic, for the time being...