In essence - should Christians demonstrate their allegiance - by wearing a Cross, for example?
Yes, they should.
Partly for reasons of witness, and partly for reasons of convenient mutual identification.
And partly because most non-Christians self-identify...
...so that devout adherents of most other religions are usually immediately identifiable - and so are anti-Christians by their style of dress (youth cult allegiance, immodesty), bodily self-mutilations, badges, consumption and conspicuous life styles.
Indeed, we have reached a situation when Christians are among the few who do not self-identify.
So we should.