The only place I've ever come across that statement is from those who love to bash Freemasons.
It may be a nice story, but it's at best unconfirmed.
Like Wayne’s son?
http://books.google.com/books?id=sIXDNotbvywC&pg=PA644&lpg=PA644&dq=%22John+wayne%22+patrick+catholic&source=web&ots=xWIlgq8zlG&sig=Yupy0SSBEwilMf6xUtrUBicUsJc&hl=en&sa=X&oi=book_result&resnum=3&ct=result