As an American, I hope you can identify strongly as an Australian. Why bother telling yourself you’re something of a European?
In any case, I hope countries form ties with Europe. Europe needs be economically stronger than it is. Better for the world, so long as they can slow their tendencies toward government control and censorship.
But there's whole communities of Americans who identify as Irish, or Anglo-Saxon, or whatever.
FYI I don’t think anyone is accepting American critique on government control and censorship right now. Maybe leave it for a decade or two.
People identify with other places, people, policies, and cultures — along with their own, or wherever they're originally from. Sometimes they don't even identify with their own, or say, feel alienated. It's perfectly fine, and in fact a very healthy state of being.