If we can divide practical reasons up into moral reasons and non-moral reasons, presumably the latter could come to outweigh the former, such that one has most reason to do the wrong thing. But that seems incoherent: insofar as you did what you had most reason to do, all things considered, you have made no practical error -- on the contrary, you did precisely as you ought to have. It's platitudinous that an immoral act is an unjustified act ("there's no excuse for immorality," we might say) so insofar as one has sufficiently good reasons to justify an action, that action is thereby shown to be morally permissible.
In other words: to say, "You morally ought to phi, but all things considered you shouldn't," strikes me as downright incoherent. The moral point of view is precisely that which takes all things into consideration. So there are no purely "non-moral" reasons, if by that it is meant a genuine normative reason that is nonetheless irrelevant to the question what you morally ought to do. If it's a reason at all, then it counts morally.
I take it people are sometimes tempted to deny this because we usually talk about moral reasons in relation to advancing others' interests, and instead call them 'prudential reasons' when the interest being advanced is our own. But can't this be explained in Gricean terms? Insofar as prudential reasons are a proper subset of moral reasons, it provides more information to specify a reason as prudential. To call it a moral reason, though technically correct, would be odd in the same way that it would be odd to call Fluffy an animal instead of a cat.
To bring out the difference, note that whether we "prudentially ought" to do something doesn't suffice to settle the question whether we should do it. Maybe there are other, non-prudential reasons, which outweigh the prudential ones. But, as noted above, the moral question is the final practical question. If something is established as morally wrong, it's off the table.
Perhaps a moral minimalist could accommodate all this whilst denying that all practical questions have moral significance. Maybe the moral reasons are primary, and cannot be outweighed, but are also limited in scope. That is, moral reasons might serve as "side constraints" to remove certain options from the table, but then remain silent on which of the remaining options we should choose. None are morally obligatory, but perhaps some of the remainder stand out on other -- e.g. prudential or aesthetic -- grounds. Such a hierarchy of reasons seems coherent (contra the opening sentence of this post), but it seems to rest on the implausible assumption that no finer-grained moral distinctions can be made besides the crude division of options into permissible vs. prohibited. That seems implausible: even among the permissible options, some might be (morally) better or worse than others. Plausibly, one might be the morally best option, the one we should pick, even if we wouldn't be blameworthy or failing in our obligations were we to pick some nearby alternative.
Is it merely a terminological dispute whether we are to say that the (all things considered) best option is thereby the morally best option too? Perhaps. But if it is a clearer way of thinking and talking then perhaps it's worth pressing the point all the same.