They could just the same have an opinion that some business that's under investigation for some crime, declare that it's unsafe for them to do their job, and just not deliver mail there ? Sorry, no; that is not an appropriate response for a paid professional.
This postal worker should rightly be sitting in jail right now.
"18 U.S. Code § 1703 - Delay or destruction of mail or newspapers
(a) Whoever, being a Postal Service officer or employee, unlawfully secretes, destroys, detains, delays, or opens any letter, postal card, package, bag, or mail entrusted to him or which shall come into his possession, and which was intended to be conveyed by mail, or carried or delivered by any carrier or other employee of the Postal Service, or forwarded through or delivered from any post office or station thereof established by authority of the Postmaster General or the Postal Service, shall be fined under this title or imprisoned not more than five years, or both."
https://www.law.cornell.edu/uscode/text/18/1703
They don't get to decide who gets mail and who doesn't. Reneging on a legal responsibility of your job is not an appropriate way to voice such a concern.
It doesn't make any sense, whatsoever, to give postal workers the ability to arbitrarily refuse to deliver mail. They shouldn't be making that decision themselves.