I can’t speak for the Navy or other services; I only have some familiarity with the USAF missile forces, and that may be somewhat outdated. Having myself served as a Minuteman missile technician, I was not oblivious to the moral quandaries of the job. My concern was less than it might have been since I served only at a testing base, not in operational silos.
However, the OP’s question is not entirely moot. The Church has not specifically forbidden Catholics to serve in nuclear weapons areas. But more recently, a group of bishops has, I believe, issued a statement to the effect that the idea of nuclear deterrence can no longer be justified. I disagree with that conclusion, but it is worth our attention.
I think that any further reduction of the nuclear deterrent would put us at risk of nuclear blackmail, and increase, not decrease, the risk of nuclear war.
In the linked article (“Sex and the Married Missileer) the Catholic airman made his peace with his duties by deciding, on a daily basis, whether it was likely, given world conditions, that he might be given an immoral launch order. If he thought that might be a possibility, he would simply refuse to report for work, and bear the consequences. (Presumably he did not believe that
any launch order was immoral. If so, his position was simply incoherent.)
But that sort of begs the question. His target might be strictly military—perhaps an isolated command center in Siberia—or it might be mixed—say, KGB HQ in Moscow. But he would have no way of knowing, since he does not, as a launch officer, know what the target is; as far as he’s concerned, it’s just a number between 0 and 99. So how would he discern a moral launch order from an immoral one?
(P.S. His concern about sexual temptation appears not entirely unjustified. In a later
incident, a male missile crew member was accused of sexual assault against a female crew member, who did not report the incident until after the end of the alert.)