A final /d/ devoicing to became a final /t/ is not all that strange. They're both alveolar stops. Now, a /g/ going to a /dZ/ is a little more strange, but still within the bounds of what could be expected in phonological change.
I think it's a spelling pronunciation. The Irish name for Saint Bridget is "Bríd", which in older times would have been spelled "Brighid", the "gh" being a voiced velar that exists in very few languages I know*. If you apply English pronunciation rules to that spelling, you get /brIdZId/, the spelling of which can then be nativised to English as "Bridget".
For comparison, take the case of the American name "Caitlin" pronounced "Kate Lynn". "Caitlín" is the Irish spelling of the name "Kathleen", and is pronounced "Kat(h)leen". But at some point a spelling pronunciation arose and what was originally an "error" became a name unto itself.
*I hear this sound when Arabic speakers say "Afghan" or "Afghanistan" - the "f" sounds like a "v" and the "gh" sounds like a voiced "h".
