Maybe as 'Catholic' by Religion
and
'American' by citizenship.

They are just different methods of categorizing. Hopefully they are not mutually exclusive. Certainly they are not mutually inclusive.

Maybe if I am talking to the Church, or in Rome, I would be an 'American' Catholic. If I'm talking to Americans, I would likely say I'm a 'Catholic' American.

Both 'identities' are important to me. Which I list 'first' depends on context.

How do you answer your question?