Not directly about moral intuitions but intuitions in general:

Sozou’s idea is that uncertainty as to the nature of any underlying hazards can explain time inconsistent preferences. Suppose there is a hazard that may prevent the pay-off from being realised. This would provide a basis (beyond impatience) for discounting a pay-off in the future. But suppose further that you do not know what the specific probability of that hazard being realised is (although you know the probability distribution). What is the proper discount rate?

Sozou shows that as time passes, one can update their estimate of the probability of the underlying hazard. If after a week the hazard has not occurred, this would suggest that the probability of the hazard is not very high, which would allow the person to reduce the rate at which they discount the pay-off. When offered with a choice of one or two bottles of wine 30 or 31 days into the future, the person applies a lower discount rate in their mind than for the short period because they know that as each day passes in which there has been no hazard preventing the pay-off, their estimate of the hazard’s probability will drop.

This example provides a nice evolutionary explanation of the shape of time preferences. In a world of uncertain hazards, it would be appropriate to apply a heavier discount rate for a short-term pay-off. It is rational and people who applied that rule would not have lower fitness than those who apply a constant discount rate.

Evolution and irrationality — Evolving Economics

In Study 1, college students’ preferences for different brands of strawberry jams were compared with experts’ ratings of the jams. Students who analyzed why they felt the way they did agreed less with the experts than students who did not. In Study 2, college students’ preferences for college courses were compared with expert opinion. Some students were asked to analyze reasons; others were asked to evaluate all attributes of all courses. Both kinds of introspection caused people to make choices that, compared with control subjects’, corresponded less with expert opinion. Analyzing reasons can focus people’s attention on nonoptimal criteria, causing them to base their subsequent choices on these criteria. Evaluating multiple attributes can moderate people’s judgments, causing them to discriminate less between the different alternatives.

Thinking Too Much: Introspection Can Reduce the Quality of Preferences and Decisions

And of course Pascal's Mugging: Tiny Probabilities of Vast Utilities:

I'd sooner question my grasp of "rationality" than give five dollars to a Pascal's Mugger because I thought it was "rational".