The non/standard distinction is also seen in the contrast between practical vs. epistemic reasons for belief. The practical benefits of a rich ideologue's patronage might provide you with non-standard reasons to believe that global warming is a hoax. But if all the evidence is against it, then you have no standard reasons for the belief, and cannot come to hold it through the direct process of rational belief formation. (You might get yourself to believe by indirect methods, of course. Again, it could be a standard reason for some such action.)
In his 'Reasons: Practical and Adaptive', Raz makes the distinction as follows:
Standard reasons are those which we can follow directly, that is have the attitude, or perform the action, for that reason. Non-standard reasons for an action or attitude are such that one can conform to, but not follow directly. (pp.4-5)
This makes it sound like a contingent empirical matter, for isn't it up to psychology to tell us what considerations humans are able to act upon? But not really. Science might tell us what considerations humans can respond to, and even cite in folk-psychological explanations of their own behaviour. But there are normative elements to action (as opposed to mere behaviour), and to genuinely following a reason (as opposed to merely taking oneself to have done so), which return us to the philosophical domain.
But now we have a problem. Suppose Bob mistakenly takes practical reasons to warrant belief. Anne offers him $100 to believe that the world is flat, and Bob manages to form the belief, citing the monetary reward as his reason. Does this mean that Bob follows the practical reason for belief? If that's possible -- if practical reasons for belief can be followed after all -- then they would (by definition) qualify as standard reasons.
Raz wants to deny this, which means that we need some independent basis for determining whether the reason was followed in such a case. (It would be circular to appeal to the fact of its being a non-standard reason to explain why it doesn't qualify as having been followed!) Recognizing this, Raz instead appeals to facts about "the nature of that reason" (p.19) to settle the matter. For example, if following a reason would be self-defeating, as in our original example, then that's a basic fact which explains why it cannot be successfully followed, and thus why it is non-standard. The case of practical reasons for belief is less clear. Raz claims (p.20):
the fact that non-epistemic reasons cannot serve to warrant belief shows that they cannot be followed. Ultimately, however, the explanation of the force of this point depends on understanding the normativity of reasons, their hold on us, a matter I deal with elsewhere.
Further direction would help. Oh well. That all seems a bit mysterious to me, so I wonder whether we might do better to just define standard reasons directly in terms of warrant. Or, if we take rationality as fundamental: standard reasons are those that our rational capacities respond to (insofar as they are functioning properly).