Speaking about peoples in America

I referred to a friend as an Islamic American today.  Someone questioned my choice of language and said do you call a Catholic a Catholic American?.. I say if they were catholic I'd call them an American Catholic.
This is my reasoning. 
Islam and Judaism come first between being named with being an American.  This is because both of these associations are a stronger association than our country of origin, though being an American is a high strong priority. That said, you say Jewish American rather than an American Jew. 
But with Christianity and say Hinduism and the other religions, its the other way around.  An American Protestant, an American Mormon or an American Hindu.  American Sikh.
The reason I promote Islam and Judaism is two fold.  1. they both endorse Modesty in their presentation. and 2. both abhor the practice of charging interest among their own peoples.  This to me is a higher association than just being a christian or whatever and so forth.  So thats the way that things seem to make sense to me.  Make sense to you?  Thanks.