Dear Romulus, context matters. In a hypothetical thought experiment, sure it is easy to choose between obeying God or man. But when one has to consider that it may cost one's job or life, not everyone has the honesty, fortitude, courage and faith of St. Thomas More. Knowing the right answer and choosing it are two distinctly different things.
In general terms, you make a valid point, and I did consider it before posting. But here we are talking chiefly of Catholic chaplains, who are in the happy position of not having wives and children family relying on them. Freed from powerful temptations to compromise, it becomes easier for them to make the right choice, one that arguably would call for greater heroism from a lay person living in the world.
To be sure, matters are being engineered in this way not so much to cow chaplains into submission as to make their continuing ministry in uniform impossible and thus drive them from view. This will present a hardship and spiritual danger to service members — but sanguis martyrum semen Christianorum.
I’m sure we agree that before going underground Catholic citizens (and all others of good will) should loudly defend their civil and human rights to practice their religion unmolested.