Well, I've been to the Vatican's website in the past. I think 2010 was the last time. It didn't trigger my subliminal consciousness.
So, after reading your comment, I went to the WayBack Machine (Archive.net) and walked it up to June 4, 2011 (the last time the previous design was there):
Sure, it's similar, but it doesn't really suggest a crescent moon and star to me. However, the newer design with the yellow glow and the removal of the circular icons inside the broken circle starts my internal radar pinging:
Maybe it's just a coincidence. However, the Vatican seriously needs to reconsider that new design!
Cheers!
Good detective work, Doctor! I have not been on the actual site in a little while, so I'm glad I wasn't blowing smoke the first time!
All in all, I'm sure it's just coincidental--the new design is "cleaner," which perhaps allows for better navigation/access to the information.