I think there is a basic problem in discussion about "Catholic Identity". 

What is it? 

How is it to be defined?

Above all, surely it is not a fixed identity, but one that must be continually forged/reshaped in response to the surrounding culture ...  to which the history of the Church bears ample evidence (for both moments when that bold reshaping enriched the Church, and for the moments when the Church impoverished itself by retreating from the world).