EWTNs World Over has its interview with Clare Asquith, author of Shadowplay: The Hidden Beliefs and Coded Politics of William Shakespeare up on its audio page. (When the sound file comes up, skip forward just over 8 minutes to get to the interview.)
I heard about Asquith's book just over a month ago, and while there does seem to be some evidence to support the speculation that Shakespeare was Catholic, any talk of hidden codes in Shakespeare sets my brain on "Suspicious". I participated off and on for years in a Usenet discussion group about Shakespeare, and between that and my other reading, I'm well aware of the phenomenon of nutcakes and their conspiracy theories about Shakespeare, which often do involve codes hidden in the plays. The author of the plays is secretly Edward DeVere and everyone in England knows it but no one is allowed to say it, so there's a massive number of coded references to DeVere's authorship concealed in the plays (presumably so everyone in the audience can nod knowingly); the author of the plays is Marlowe, the author is Bacon, the author is Queen Elizabeth's illegitimate son, the author is Queen Elizabeth's lover, the author is Queen Elizabeth, etc. Many of the people who hold these views are out-and-out fanatics--can't change their mind and won't change the subject--and are sometimes rather too much like the other conspiracy theorists (for example, Area 51 or obsessive JFK assassination people) for comfort.
Asquith, however, sounds surprisingly sane and well-balanced. She says part of what opened her mind to this view of Shakespeare's plays was seeing how seemingly innocuous plays were used to convey dissident political messages in the Soviet Union. (Other reasons were her own English Catholicism and the new, non-Protestant takes on English history of the time.) She makes the idea of discreet Catholic references seem reasonable. I still don't wholly buy it, because, besides the danger of publically supporting Catholicism over Protestantism (which meant questioning the legitimacy--in both senses of the term--of the Queen), I just don't think playwrights work that way. There may be a little something to what she's alleging and, even if there's not, her book may provide an interesting look at Catholic sympathizers in Elizabethan society, so I am open to reading it--not buying it, but reading it.
For a World Over program about Shakespeare's possible Catholicism, listen to the interview with Dr. Paul Voss (production date 8/17/01.) It provides an easy, enjoyable introduction to the subject and also explains in passing why Calvinists never wrote tragedies.