Why should it be irrational to love somebody after their death? You can still listen inside of you and discover more things about that person - what you missed, what you would wish to do with them now, whatever. I don't think that requires some mystical belief that the dead person's spirit is somehow still around (other than in your own neurons).
Humans are no "classical computers", we have emotions and desires built in (for a purpose, but still). It is not necessarily rational trying to suppress those and aiming to become as much as a calculator as possible. You could as well just go for the ride and see where it takes you.
It is not irrational to love someone after their death, but it is fairly irrational to refuse to love anyone else after your wife dies and it is very irrational to write sealed letters to a dead person.
It shows that Feynman was quite willing and able to surrender to irrational behaviour when he wanted to. The difference between Feynman and the superstitious man was not a rejection of things irrational, but a conscious control over when to give in to the irrationality and when to remain scientific.
Of course, you might say that this is only sensible - but many people who take a reductionist view ("there is nothing beyond the material") explicitly reject this balance.
>it is very irrational to write sealed letters to a dead person.
It seems irrational when you presume that the only purpose of a letter is to be read by the recipient. But writing a letter can help clarify your own thoughts and feelings, which is a perfectly rational thing to want to do.
Have you really never written something down just to clarify your thoughts? It's legitimately useful. Usually I don't do it by writing a letter to someone, but I could definitely see doing that in Feynman's situation.
Humans are no "classical computers", we have emotions and desires built in (for a purpose, but still). It is not necessarily rational trying to suppress those and aiming to become as much as a calculator as possible. You could as well just go for the ride and see where it takes you.