While certainly a private thing that gave him happiness or solace or peace in life, I'm confident that he chose to include it in his collected record on death.
This seems consistent with everything that (I imagine) I know about him from reading his own autobiographical stuff, as well as other peoples' attempts.
(Aside: Klaus Fuchs, the guy whose car he borrowed, turned out to be the mole at Los Alamos, and that car was instrumental in the performance of Fuchs' activities.)
I know you're not talking about legal matters, but some of the issues behind libel and speech law are derived in part from moral concerns.
As a side note, it's not all together clear that it would be illegal to publish something like this were he still alive, as he would be considered a person of public interest.
Now, the issue of whether it's bad? That's strictly a taste thing. Had the author of e biography chosen to publish any and all seedy letters found in Feynman's private collection, I think we could agree that that is "bad", as in, bad taste...but I think the case could be made that the publishing of this type of personal letter is not in that same category, in terms of taste