Beliefs may inherit the irrationality of other beliefs they are based on. (If I irrationally believe that p and that if p then q, and so conclude that q, then this validly derived belief likewise lacks rational warrant.) What about acts or desires that are based on irrational beliefs?
Parfit (On What Matters, chp 5) discusses the case of a man who irrationally believes that smoking would be good for his health, and on this basis desires to smoke. I think this desire is irrational, since it should be clear (given his evidence) that in fact he has every reason not to smoke. This fact about his evidence makes the agent liable to rational criticism if he smokes: doing so is "stupid", "unwise", "foolish", etc. -- though of course the agent himself might fail to realize this.
But instead of assessing the rationality of desires/actions against the agent's evidence, Parfit claims that desires (acts) are rational iff they are based on beliefs which, if true, would provide sufficient reasons to so desire (act). Since if it were true that smoking is good for your health, this fact would provide sufficient reason to [want to] smoke, Parfit concludes that the act/desire is rational even though the belief is not.
I find this puzzling. Since it is irrational for the agent to believe that smoking is good for his health (and we may stipulate that there aren't any other relevant considerations), it is presumably likewise irrational for him to believe that he has any reason to smoke. He rationally ought to believe that he has no such reason, and hence that smoking is irrational for him. This normative fact seems to conflict with the claim that in fact smoking is rational for him. Consider the following principle of rational transmission:
(RT) if S rationally ought to believe that it is irrational for her to Φ, then it is irrational for her to Φ.
One might respond by arguing that the act only becomes irrational once S actually has the beliefs that she ought to have. That is, we should merely grant the weaker claim:
(RT-actual): if S believes (as she rationally ought) that it is irrational for her to Φ, then it is irrational for her to Φ.
Since the smoker doesn't have this rational belief, but instead irrationally believes that he ought to smoke, it may be claimed that in these circumstances it is perfectly sensible of him to go ahead and smoke. But that doesn't sound particularly sensible to me. (Sure, it's consistent with his irrational beliefs, but acting in ways consistent with irrational beliefs is not necessarily sensible.)
Parfit says, "Our claim should be only that, since these irrational beliefs are false, [the smoker has] no reasons to act in [this way]." But this seems too weak. Suppose the evidence is misleading and it turns out that smoking actually is good for your health after all. So it turns out that the smoker does have objective reason to act in this way. Still, his act is irrational (unwise, stupid, etc.) since all his evidence suggests that he would do better not to smoke. Even if he turns out to be lucky, we can -- contra Parfit -- still criticize his act. It wasn't rationally warranted, given his evidence.
Curiously, Parfit grants something close to this. He writes: "We should still claim that, when I want to smoke, I am being irrational, but the irrationality is in my belief, not my desire." But what does it mean for a person to be irrational "when" they X, but that the irrationality is not "in" their X-ing? We might take it to simply mean that they exhibit some (possibly unrelated) rational flaw at the same time as they X. But again, this seems too weak.
Suppose that I'm in the midst of eating dinner when I form the desire to smoke. It would be misleading to say that "when I eat dinner, I am being irrational". It's literally true, in a sense: I am being irrational at this time. But the irrationality is in no way related to my eating dinner. Rather, I'm irrational in forming the desire to smoke. There's an important asymmetry in the rational significance of these two events, which isn't captured merely by noting that they are concurrent with my having an irrational belief. The irrationality of the belief infects the related desire, in a way that it does not infect my unrelated act of eating dinner.
So it looks like we need to say something stronger than that the agent is "being irrational" merely concurrently with their wanting to smoke. The connection is tighter than that. They are specifically irrational for wanting to smoke (not for eating dinner, or whatever else they might be doing at that time).
It's true that the irrationality here is merely derived from the irrationality of the basing belief. So there's a sense in which the desire doesn't introduce any further irrationality that wasn't already there. (Unlike, say, if the agent had taken his irrational belief that smoking is healthy to be a reason for jumping off a building. Then his desire would be irrational in an entirely new and further respect.) But this is just like the uncontroversial epistemic case, where my concluding that q doesn't introduce any further irrationality that wasn't already present in my prior beliefs (that p and that if p then q) -- unlike, say, if I had concluded in some unrelated proposition r.
Inherited irrationality need not make you "more" irrational, on some global scale, than you would otherwise have been. It's just to say that the downstream states or actions lack rational justification, just like the upstream states on which they are based.