In the book, the war takes place in the early 1960s (in fact, although Miller didn't intend this at the time of course, you could imagine the situation resulting from the 1962 Cuban Missile Crisis having a more disastrous outcome), so all the points about the removal of the Latin Mass don't really play into it. In fact, pointing out that the removal of the Latin Mass makes the book feel dated seems odd when compared to the fact that book depicts the aftermath of a nuclear war that never happened, a rather larger anomaly if you are taking the book on a literal level.

A CANTICLE FOR LEIBOWITZ is thus an SF story set in the future of an alternate history (rather like the FALLOUT and BIOSHOCK computer games, or Arthur C. Clarke's 2001 and 2010, which we have already supersceded) rather than a book set in our direct future. Just as the literary and philosophical points an overt alt-history might be trying to make aren't invalidated by the events never happening, I don't see how they are in LEIBOWITZ's case.

The points Miller are making tie into the faith vs. science questions and arguments such as the one between the abbot and the doctor in the last part about euthanasia, debates that are extremely relevant and fresh today.